Do you have free analog pins ?
You might be able to use 1 analog pin to register 12 keys, but you'll certainly be fine if you have 2 analog pins left.
That means another approach and no matrix.
It also means you can only press 2 buttons simultaneously (one of each analog pin), but you can't press multiple keys with a matrix either (well, you can press those buttons of course, but you can't read them correctly in that case).