I'm quite familiar with these niggers. They are a nuisance. However, not too hard to trap. Give them about an hour ride in any direction away from your property and they won't be back.
Based gopher, just don't let them dig under your foundation or any of your out buildings.
Looks like a Nutria. I know people hunt and eat those things.
Dang that is a healthy looking yard! You're going to need at least a 22 magnum to tend that. Rabid animals happen. Regarding that cute little thing; you cannot have one withing 150 yards of a structure. It will take a couple of years but eventually you will be asking, "Does fire kill it? How do I kill it with fire?" Have been there. Have done that.
Find its main hole and drain the gas from an oxy-acetalene torch down it, add a bit of fire and your gopher problem is gone. It'll also aerate your lawn at the same time!
Gasoline in the top hole and light a fire at the bottom hole, then wait. Safe distance is a lot further away then you would think. CO2 will do it with a lot less boom suspense.