Even if you dug it deeper (and that would be work) I wouldn't put koi in. If you are in love with the brightly colored fish LIKE koi I would just get a few goldfish. Right now I have about 8 being quarantined and conditioned (so they are in good shape when they get in my pond) in a 20g tank. If you look through the feeder goldfish tank you can find some really lovely ones. I have a pure white one, two red and whites, an orange and white, a black and yellow, a black and orange, a plain old orange and a rosy bronze colored one. You just have to take the time to look. Mine are very active and I love them. In fact I like them so much that, since they will be out in a pond, I got a lionhead so I could have goldfish inside. He goes in the 20 when the other goldfish go outside. I know there are people here that don't care much for goldfish, but I think they are adorable (some are more than others--I'm not a big fan of eyes sacs. But then it really is just opinion) and they are so innocent. They make me feel like I'm little again. I mean how many of us started originally as kids with goldfish bowls? I know I did. That's why I try to give a few of those poor, mistreated goldies a good home now that I know that a one gallon bowl is not big enough for goldfish. I feel guilty for all the goldfish I've killed.
Anyway, sorry I got off on that. It's just I had been thinking for a long time that I didn't like goldfish, and when I actually got some again, I loved them.
P.S. If you have plants (read: lots of plants) and only keep a few goldfish, you will be okay without a filter. Maybe 3 goldfish and a school of rosy reds?