The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+145x^10+106x^11+565x^12+624x^13+1442x^14+1648x^15+2577x^16+3560x^17+3431x^18+4436x^19+3514x^20+3688x^21+2580x^22+1632x^23+1406x^24+568x^25+583x^26+114x^27+129x^28+8x^29+10x^30+1x^34

The gray image is a code over GF(2) with n=38, k=15 and d=10.
This code was found by Heurico 1.16 in 13.7 seconds.