The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+147x^22+209x^24+181x^26+177x^28+143x^30+114x^32+39x^34+11x^36+2x^38

The gray image is a code over GF(2) with n=54, k=10 and d=22.
This code was found by Heurico 1.16 in 0.832 seconds.