The generator matrix

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

generates a code of length 16 over Z4 who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+64x^9+172x^10+250x^11+390x^12+674x^13+930x^14+1034x^15+1095x^16+1090x^17+954x^18+702x^19+410x^20+214x^21+118x^22+62x^23+24x^24+6x^25+2x^26

The gray image is a code over GF(2) with n=32, k=13 and d=9.
This code was found by Heurico 1.16 in 2.07 seconds.