The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+30x^13+168x^14+226x^15+499x^16+864x^17+1326x^18+1822x^19+2543x^20+3192x^21+3648x^22+4024x^23+3666x^24+3308x^25+2540x^26+1904x^27+1342x^28+746x^29+488x^30+214x^31+138x^32+52x^33+22x^34+2x^35+3x^36

The gray image is a code over GF(2) with n=46, k=15 and d=13.
This code was found by Heurico 1.10 in 7.61 seconds.