The possibilities in my estimation, in the past ages, are as follows:
1. A steppe horde: This group, can often remove the necessity of "money" (as in coins or state defined currencies), governments, there is already common ownership of production which is divided up equally or by participation as loot or people are pastoralists and the land is not owned, etc... So, the Western Scythians for instance, could fulfill this role in the previously mentioned modes in their traditional homelands in the Pontic steppe. Other hordes could achieve this similarly in their own territories, assuming that communism does not prohibit raiding, pillaging and so forth. The issues with this venture, is that the steppe horde most likely will develop some sort of class structure due to the constant wars they generally partake in lead to different results and certain warriors gather greater and greater amounts of loot, leading to the rise of a noble-warrior class that command others. Further, the capture of slaves and loot, lead to the creation of class, and from what we know of steppe hordes and even the other pre-Roman Eurasian peoples north of Greece, they tended to love jewels, amber, gold, slaves and other trinkets that they adorned themselves with to an array rivaling the most stratified societies on the planet at the time. We also come across the issue that these steppe hordes is that they did possesses property, defined perhaps as personal property, but did not possesses property over the land. Due to the nature of this personal property, which is humans, horses, precious jewelry/stones, trophies and clothing, this is not a personal property that could lead to communism. The main allure though of this group, is unlike other options, these hordes can defend themselves perfectly well until the modern era and they have no conception of land ownership. 3/4
2. A Bandit confederation: This was a style of political organization that developed in several locations in history. The most famous example of this in my study, is the Sawad pirate-bandit confederation that ruled the swamplands of southern Iraq after the end of the Zanj rebellion and the Qarmatian menace. In this republic, we know that they did not really have a government other than sort of appointed commanders and imams, which were not wholly differentiated from others. These pirates for several decades held great power in the region and inflicted losses on both the Buyyid and Abbasid states before they were broken up over time by the later Buyyid and Saljuq regimes. This grouping is effective for the proto-communism in that it has a distaste for the general nobility, the ruling castes and the conception of working for other classes, thus they have a sort of class struggle mentality already (at least to a degree). Further, such pirate confederations do not support private ownership and things become communal via common sharing of loot and shared placement in class. Pirates and bandits however, in all cases that we know of when forming into states, continue to use currency and do not barter as steppe hordes or similar groups do. Rather, these conglomerates are tied to the economic system that requires them to gain loot to then use to purchase other items; it is not like the steppe hordes which looted in an effort to hoard these items as symbols of victory. Pirates and bandits also have an issue that their lifestyle and usage of currency leads to the creation of social classes by who can purchase more and or have the best cadre of fighters. This group often also exists on the margins of established empires and powers of sedentary states, should this sedentary empire end, the pirate/bandit confederation begins taking taxes in their name and the state reforms...So, 1/4-2/4
3. A Peasant Republic: A fan favorite among socialist thinkers, this is one where a class of peasants either exist primordially holding the lands they live/farm on or overthrow the elites who prior were over them. This situation is a sort of communal republic, peasants who meet for communal issues and have no currency, government, social classes and no private property over means of production. This group however, is less feasible due to its poor prospects for survival outside of high mountains, but this is unlikely due to the fact that no large agricultural society occurs in places that are so defensible that agriculture is poor. Regardless, as
@lefthandhummingbird mentioned, it is difficult to consistently defend your culture against heavy cavalry and heavy infantry, with only light infantry and disorganized even zealous infantry. In the past, the conquests of powerful Mesopotamian states often came at the expense of small localized peoples who had villages and a raiding culture, these may have had no currency, private ownership and so forth, but were nonetheless inferior to the larger states in the region when it came to war making. The best way to solve the issue of weakness would be to have a sort of government control the resources and promote a highly disciplined military, similar to say the idealized Republic of Plato.
4. A Platonic ideal: The idea would be a state where there is a government of bureaucrats and an empire who held the position of divine entity and all land was owned by this entity and given out in usufruct to all the people. This ruler then due to some sort of custom or restraint, does not develop currency of their own and does not permit social classes. Some ideas for this sort of state would be perhaps in Egypt prior to large scale horse-camel domestication, pre-columbian California, or some sort of fertile island; all instances where the main defense is geography.