Forrestal class? No. Not enough depth. It is important to keep in mind that the hull doesn't sit on the floor of the graving dock, it sits on bracing and supports (aka: keel blocks)that are massive enough to allow work crews and equipment to get UNDER the hull as it is constructed. 12 meters over the sill simply won't work, you would need at least 14, with 15 or 16 being a better option, especially since the keel blocks are close to 3 meter tall in this particular dock.
Width is questionable as well, although it isn't a compete stopper. Be sort of like building a ship in a bottle, except the parts would weight 100 tons.
It would probably be possible to expand the dock's capacity, but that would also require a deeper channel to be dredged and maintained.