Ulla, as great the predator solution might sound, I live on several acres where gophers rule. There are lots of predators, hawks, owls, bobcats, foxes, etc., that spend their days/nights looking for food, and I have yet to see fewer gophers, ever, in 30+ years.
There are owl/hawk poles you can install that need to be 10+ feet above the ground,
should have a cross-piece at the top so they can sit and watch. Once they catch a gopher or
mouse, they want to fly to a protected place to eat it, like big tree branches, so that combo will do something, but not nearly enough. I have noticed that they get the
rabbits that get past the
fence on occasion, but the rabbits have fewer places to hide in my garden than in their brush-covered habitats.
Don't know how big your garden is, or how much the soil freezes in the winter (mine doesn't,) I have started lines of asparagus/narcissis/dock weed going down the fenceline, just trying to wall them out. I started at the most active places where they came under the
fence, then spread along the fenceline from there.
Asparagus has a huge root system they avoid, can live for 20+ years, it a tough plant. Clip off the spears as they appear so it will grow and produce more, making more roots. If it is left on the plant, it turns into a fern right away and doesn't get as big as it could.
If you notice a native weed in your area that the gophers leave alone, doesn't compete with your plants or isn't too invasive, it could help be a part of that
underground barrier. Narcissis bulbs multiply faster than daffodils, those can be tucked into that line.
Elephant garlic is fabulous, and is a great companion plant to roses and a lot of other plants.