The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+42x^13+125x^14+292x^15+499x^16+810x^17+1318x^18+1864x^19+2522x^20+3156x^21+3658x^22+3976x^23+3810x^24+3300x^25+2588x^26+1808x^27+1244x^28+834x^29+481x^30+244x^31+114x^32+50x^33+22x^34+8x^35+2x^36

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 20.4 seconds.