The generator matrix

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

generates a code of length 27 over Z4 who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+30x^15+126x^16+290x^17+487x^18+836x^19+1317x^20+1944x^21+2851x^22+3842x^23+4775x^24+5862x^25+6735x^26+6836x^27+6706x^28+6100x^29+5034x^30+4062x^31+2911x^32+2018x^33+1329x^34+728x^35+409x^36+164x^37+75x^38+50x^39+11x^40+6x^41+1x^42

The gray image is a code over GF(2) with n=54, k=16 and d=15.
This code was found by Heurico 1.10 in 43.6 seconds.