The generator matrix

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

generates a code of length 19 over Z4 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+46x^10+102x^11+229x^12+436x^13+558x^14+908x^15+1328x^16+1612x^17+1894x^18+2024x^19+2004x^20+1684x^21+1302x^22+948x^23+590x^24+356x^25+164x^26+114x^27+71x^28+8x^29+4x^30+1x^32

The gray image is a code over GF(2) with n=38, k=14 and d=10.
This code was found by Heurico 1.10 in 1.22 seconds.