It's quite feasible to keep 3 or 4 birds in the space you say ..Get an 8x4 shed and put on the side of it an 8x4 outside run. Put plenty of shavings on the floor of the shed, Clean it out regularly. Hang a cabbage or a bunch of tied brassica leaves on a string suspended from the roof inside the shed.On the 4ft wide back full width of the shed , build in 2 next boxes on top of these put a wider piece of board than the nest boxes, on the top of this at each end fix a piece of wood say 3x4 or 4x4 on the edges across it back to front, then fix a piece of handrail etc on top of this so its running across the full length of your board this becomes their perch. The wide top under this becomes their dropping board which can easily be cleaned off daily..
Dig your outside run over frequently,scatter them their corn in the run too and pop em a grass sod or two in there when you can ... I think 3 or 4 hens would be quite happy in such a set up..