The generator matrix

1 0 0 0 0 1 1 1 1 0 1 2 2 0 2 1 1 0 1 0 2 2 1 2 1 2 1
0 1 0 0 0 0 0 0 0 2 2 1 1 1 1 2 1 1 3 2 0 1 3 1 2 0 3
0 0 1 0 0 0 1 2 3 1 0 0 0 2 1 2 3 1 1 1 2 3 2 2 3 2 3
0 0 0 1 0 1 2 0 3 1 3 1 3 2 1 0 2 1 0 3 2 1 3 3 1 1 3
0 0 0 0 1 2 0 1 3 1 1 1 0 3 3 3 1 2 2 2 1 3 0 1 0 2 3

generates a code of length 27 over Z4 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+152x^22+195x^24+200x^26+163x^28+144x^30+112x^32+48x^34+9x^36

The gray image is a code over GF(2) with n=54, k=10 and d=22.
This code was found by Heurico 1.10 in 0.062 seconds.