You provided a bit of new information. I had envisioned something much smaller. If it is going to be that size, I'd suggest looking at height. You want to be able to walk inside it. Trust me on that. I bounce up and down when I walk. You don't want it just barely taller than you. You want some head clearance.
I like the size of that run, but a 16.4 foot span is a long way to span. You either need some really heavy lumber to support that span or you need some supports in the middle. 45 mm (2") squared lumber will not do it. With a solid roof, you need to consider snow, ice, and wind load. Even with a wire roof you need to consider snow and ice load. I made my run 12' wide, but I had the lumber available after a wind storm took out a shed roof. I don't know what standard lengths your standard building material comes in, I'd guess around 8', but if you are buying material, you might consider that standard width as your maximum width. Just build it longer.
You might discuss this with the company that supplies those runs. They may not want to stick with the 45 mm lumber if they know the size you envision.
Another thing. I'd suggest you look at aprons for protection from digging predators instead of burying wire straight down. Attach a boundary of wire fencing around your run or coop and run, depending on your final layout, but lay that wire horizonbtal instead of burying it straight down. The idea is that a digging predator starts digging at the fence line and hits the wire. It does not know to back up. You don't absolutely have to bury it at all, but many people skin the grass back, lay the wire, and put the turf back. This gets it totally out of sight and away from lawn mowers and weed eaters. About a half meter width of fencing is plenty and this is a lot easier than burying the wire, especially if you have rocky ground. I personally think it is more effective too, but that is just an opinion.