Excellent.
This isn't that large. You can get conventional lumber at your big box stores to frame out a roof with that span.
Why use hardware cloth when you can just put a solid roof on it and not have to clean anything off and not have to mess with tarps to try to keep the run dry?
Where are you located in general? It's best to update your profile with that information. For this thread, we'd need to know about live loads that your roof may experience and the soil heave on which your structure will be built.
I'm in snow country with a code footer depth minimum of 42". I also converted a large shed into a coop and built a large run off of it. My run is 12' x 24' with an 8x4' jog off the back of the coop.
I dug 42" holes for concrete piers to anchor 4x4 PT posts to at 8 ft on center then topped the two supporting walls with doubled 2x6 beams to support 14'x2x6 rafters with the tails hanging off the front and back to offer a little overhang to keep water from running down the walls. I added 2x4 PT supports at 4ft on center between the posts to support 4' wide strips of 1/2" hardware cloth on the walls and out 18-24" over the ground for the predator apron.
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I decided on asphalt shingles for the roofing material but metal roofing could also be used depending on climate and the amount of shade offered at the build site. I wouldn't recommend metal roofs in the blazing sun because they will radiate heat down into the structure.
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