The generator matrix

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

generates a code of length 19 over Z4 who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+72x^11+214x^12+376x^13+612x^14+918x^15+1197x^16+1594x^17+2060x^18+2166x^19+2056x^20+1802x^21+1276x^22+850x^23+586x^24+318x^25+148x^26+90x^27+42x^28+6x^29

The gray image is a code over GF(2) with n=38, k=14 and d=11.
This code was found by Heurico 1.16 in 6.77 seconds.