Well, you could:
Build a square 11ft.x11ft., with one side open, 5' 1/2ft. tall, with support in the middle of each 11ft. 2x4 in the form of a 5' 1/2 ft. 2x4, made from cutting one of your 11s' in half. You know have this:
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Then build two more 11ft. x 5' 1/2ft. sections, making this:
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And make all the corners a 6ft. long 4x4, (which, unfortunately, you will have to buy, because a 2x4 isn't enough support..) which will leave you two 11' 2x4s to use as support for whatever net type top you decide to put on. Then just put on some sort of wire around it. Chicken wire will not prevent foxes, coyotes, or racoons, so go with a stronger type if you want to make your run secure, and build an apron of wire extending a foot or two out from the bottom of the run. A wild bird net across the top will keep your hens in and owls out, but racoons (if hungry enough) will climb up there and tear through it, so make sure your girls are locked up at night. This will give you 154sq.ft., enough for 14-15 hens.
Of course, you don't have to have 2x4s across the ground, so you could do a 22'x22' run, with eight 4x4 corner posts/between posts and three 11' 2x4s leftover to build a door with, or something. The second run would have 484sq.ft., which is enough room for 48-49 hens.
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As for covering part of the run, you could use some of those corrugated see through roofing panels, just not the PVC type because it cracks in the sun.
Hope you are still awake, and this was informative and helpful not brain-dead boring. Good luck! Tell us what you end up doing!