Half-inch steel hardware cloth attached to the bottom of raised beds is an effect barrier against gophers and burrowing rodents. Hardware cloth is available at most hardware stores in 3 and 4 foot wide rolls and can be cut to length using metal shears. Be sure to wear gloves, as the cut edges can be sharp. Bend the edges of the material so it lays flat against the inside walls of the planter, and use a staple gun to secure it in place. Use staples every few inches so there are no gaps a gopher can squeeze through.
Remember that root crops such as carrots and beets can’t grow through the screen bottom, so build raised beds that are tall enough to provide root space for plants.