The generator matrix

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

generates a code of length 25 over Z4 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+38x^13+141x^14+290x^15+561x^16+860x^17+1357x^18+2158x^19+2958x^20+3994x^21+4876x^22+5722x^23+6523x^24+6640x^25+6407x^26+5748x^27+4904x^28+3922x^29+2989x^30+2222x^31+1422x^32+884x^33+467x^34+238x^35+138x^36+46x^37+18x^38+6x^39+5x^40+1x^42

The gray image is a code over GF(2) with n=50, k=16 and d=13.
This code was found by Heurico 1.10 in 32.3 seconds.