If you plan on having a movable style coop, not sure how you'll prevent digging. I had an injured bird in a rabbit hutch just set on the ground and dig have something attempt to dig under a couple times.
I buried 2x10's around our large coop perimeter along with 2' wide stamped pavers around 3 of the 4 sides. I haven't had any issues with digging predators.
As Marv shared his story above, you'll need more than just screens on the sides. I recommend 1/4" welded wire and framed with lumber.
Your dimensions are plenty of room for 4 birds. We have 8 in a similar sized run and a 4x4 roosting area. We can but don't close the run off from the roosting coop unless it's really cold.
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