The generator matrix

1 0 0 0 0 0 1 1 1 1 0 0 1 2 2 1
0 1 0 0 0 0 0 0 1 1 1 2 0 2 1 3
0 0 1 0 0 0 0 1 0 2 3 1 1 2 0 3
0 0 0 1 0 0 0 1 1 2 2 3 2 1 1 3
0 0 0 0 1 0 1 0 1 2 3 2 2 3 1 2
0 0 0 0 0 1 1 3 2 3 1 2 3 1 0 3
0 0 0 0 0 0 2 2 0 2 0 2 0 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+66x^9+153x^10+260x^11+456x^12+628x^13+849x^14+1076x^15+1140x^16+1112x^17+931x^18+652x^19+427x^20+236x^21+115x^22+60x^23+23x^24+6x^25+1x^28

The gray image is a code over GF(2) with n=32, k=13 and d=9.
This code was found by Heurico 1.10 in 0.237 seconds.