I definitely can help you with a 4x4 design; however as my wife would put it... It's Built Like Fort Knoxs (and not very price effective). Included a few pics below:
Now if I had to redo it and if I was on a budget, I would probably do something with Cow Panels and there are two great videos Id suggest watching below:
and
Materials Suggested
Feedlot Panel (Cow Panel), 16 ft. L x 50 in. H ($22 each)
I would get 4 panels (2 for coop and 2 for a run)
2 gives you 100" (8.3') and slightly overlap panels.
Treated 2x4x9's ($8.27 each - Need 4 just for coop
Chicken Wire - (Wrap Cow Panel) - 36x150' = $69.99
Tarp 16'x20' = Cover Top of Coop = $31
Overall it should be about $200 or less
Basically, build a wooden box and keep the spacing 8'
and bend panel (which will give you a head clearance of 6.13')
Clip together (as in video) and use scrap 2x4's as roost bars.
For those interested, here is the spacing (arch bend) to head clearance for a 16' cow panel
14' = 3.5'
12' = 4.83'
10' = 5.63'
8' = 6.13'
6' = 6.63'