The generator matrix

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

generates a code of length 24 over Z4 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+58x^13+180x^14+356x^15+673x^16+1124x^17+1800x^18+2752x^19+3800x^20+5148x^21+6398x^22+6980x^23+7134x^24+6860x^25+6204x^26+5164x^27+3976x^28+2854x^29+1772x^30+1064x^31+648x^32+336x^33+156x^34+68x^35+24x^36+4x^37+2x^38

The gray image is a code over GF(2) with n=48, k=16 and d=13.
This code was found by Heurico 1.10 in 36.4 seconds.