If you can sink posts into the ground, it is easy to build a run. Although putting a roof on it requires a bit more engineering (thus more expense) and is likely to be treated as a structure or shed type thing so you'd want to make sure whether that was ok to do. Alternatively instead of putting a solid roof on the run you could just put a small portable enclosed coop in there.
If you are forbidden to sink posts into the ground, it can still be done, either by using a storeboughten dog kennel (you know, the preframed chainlink panels that bolt together at their corners) or making your own panels with wood frames and wire attached on them. Same deal with the roof issue.
If there are foxes or loose dogs about, you may ought to think about adding a several foot wide apron of stout wire mesh on the ground just outside the run fence to discourage predators digging in.
Good luck, have fun,
Pat