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Sounds quite ample. We have a supersized pen/tractor (we couldn't move with out 2 people) with a 8x3 roosting area, nest boxes, with a yard of about 8x10 covered with hardware cloth and clear heavy plastic in the winter. Summers its removed. They have another outside area that is a bit more then the "tractor" and it has an odd shape as we are using the bantam cochins as stump removal and finding the bugs in the old stump. Oh, and we have 6 bantam Cochins and that is still ample space for them. (mind you they are short and wide
what kind of bantams, oeg's or japanese would do fine with 4-6 in a 4x4 pen depending on the aggression levels of the birds. i have a trio of oeg's in a roughly 2.5x4 split off section of the coop and they only get the run 1/2 the days and their fine. bigger bantams, or more aggressive and active breeds will most likely need more space. But in general for most bantam's 4x4 should be fine.
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they actually should have more than 1 sq ft per bird, but the dimensions aren't set in stone and can be played with depending on the birds, run size, set up of the coop etc...
If it's a coop with an attached run then bantams need 2 sq ft/bird of coop space plus additional run space. If it's a breeding pen and they won't be let out then they need 4-5 sq ft/bird. So for 8 bantams you would need a pen that's 32-40 sq ft. A 4x4 pen is 16 sq ft and could comfortably house 3-4 bantams.