The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+30x^9+81x^10+140x^11+223x^12+328x^13+403x^14+496x^15+596x^16+552x^17+473x^18+364x^19+197x^20+112x^21+65x^22+24x^23+7x^24+2x^25+2x^26

The gray image is a code over GF(2) with n=32, k=12 and d=9.
This code was found by Heurico 1.10 in 0.063 seconds.