The generator matrix

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

generates a code of length 27 over Z4 who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+22x^17+156x^18+250x^19+351x^20+530x^21+712x^22+1004x^23+1154x^24+1412x^25+1630x^26+1684x^27+1784x^28+1580x^29+1262x^30+952x^31+681x^32+486x^33+318x^34+194x^35+121x^36+66x^37+18x^38+12x^39+4x^40

The gray image is a code over GF(2) with n=54, k=14 and d=17.
This code was found by Heurico 1.10 in 3.37 seconds.