The generator matrix

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

generates a code of length 18 over Z4 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+46x^13+105x^14+106x^15+69x^16+106x^17+176x^18+110x^19+48x^20+98x^21+102x^22+38x^23+10x^24+6x^25+2x^27+1x^30

The gray image is a code over GF(2) with n=36, k=10 and d=13.
This code was found by Heurico 1.16 in 20.1 seconds.