The generator matrix

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

generates a code of length 23 over Z4 who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+64x^15+148x^16+264x^17+375x^18+444x^19+609x^20+778x^21+887x^22+928x^23+957x^24+870x^25+645x^26+492x^27+315x^28+182x^29+133x^30+56x^31+18x^32+18x^33+8x^34

The gray image is a code over GF(2) with n=46, k=13 and d=15.
This code was found by Heurico 1.10 in 0.714 seconds.