One of the challenges you will discover with a small square, and going "vertical" ... is that chickens aren't helicopters ... they need atleast, if not more horizontal room, for landing, as they are flying down from the high roost ... one way to kinda help with this ... is to build ramps that they can walk up and down ... but, they really need to be 10"-12" wide ... so you just reduced your 4' coop, to 3' ... 
If you still want an elevated, reach in style coop ... I'd recommend stretching one side to 6' at minumum, 8' would be much better ... with two 3' wide doors on one side, it would still be possible to reach in and clean ... and it would increase your under coop covered runs space too!

If you still want an elevated, reach in style coop ... I'd recommend stretching one side to 6' at minumum, 8' would be much better ... with two 3' wide doors on one side, it would still be possible to reach in and clean ... and it would increase your under coop covered runs space too!
