The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+92x^13+276x^14+546x^15+994x^16+1638x^17+2551x^18+3692x^19+5033x^20+6558x^21+7609x^22+7784x^23+7352x^24+6344x^25+5106x^26+3884x^27+2634x^28+1652x^29+946x^30+470x^31+237x^32+98x^33+23x^34+8x^35+5x^36+2x^37+1x^38

The gray image is a code over GF(2) with n=46, k=16 and d=13.
This code was found by Heurico 1.10 in 35.9 seconds.