The generator matrix

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

generates a code of length 24 over Z4 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+12x^13+86x^14+174x^15+389x^16+576x^17+881x^18+1318x^19+2039x^20+2532x^21+3011x^22+3490x^23+3590x^24+3636x^25+2978x^26+2664x^27+2046x^28+1272x^29+900x^30+526x^31+372x^32+156x^33+77x^34+18x^35+11x^36+8x^37+3x^38+2x^39

The gray image is a code over GF(2) with n=48, k=15 and d=13.
This code was found by Heurico 1.10 in 7.73 seconds.