The generator matrix

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

generates a code of length 23 over Z4 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+34x^13+133x^14+266x^15+517x^16+862x^17+1274x^18+1890x^19+2484x^20+3180x^21+3711x^22+3868x^23+3843x^24+3252x^25+2580x^26+1916x^27+1224x^28+818x^29+475x^30+250x^31+118x^32+46x^33+18x^34+2x^35+4x^36+1x^38+1x^40

The gray image is a code over GF(2) with n=46, k=15 and d=13.
This code was found by Heurico 1.16 in 15.5 seconds.