The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+82x^17+192x^18+416x^19+709x^20+960x^21+1358x^22+1866x^23+2501x^24+2976x^25+3369x^26+3652x^27+3482x^28+3164x^29+2544x^30+1896x^31+1445x^32+910x^33+558x^34+348x^35+177x^36+100x^37+42x^38+14x^39+5x^40+1x^42

The gray image is a code over GF(2) with n=54, k=15 and d=17.
This code was found by Heurico 1.10 in 12.9 seconds.