The generator matrix

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

generates a code of length 19 over Z4 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+56x^13+102x^14+132x^15+189x^16+182x^17+214x^18+268x^19+244x^20+222x^21+178x^22+108x^23+74x^24+50x^25+18x^26+4x^27+4x^28+2x^29

The gray image is a code over GF(2) with n=38, k=11 and d=13.
This code was found by Heurico 1.10 in 0.046 seconds.