The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^13+100x^14+134x^15+199x^16+220x^17+200x^18+198x^19+239x^20+252x^21+196x^22+114x^23+72x^24+52x^25+16x^26+2x^27+1x^36

The gray image is a code over GF(2) with n=38, k=11 and d=13.
This code was found by Heurico 1.16 in 12.2 seconds.