The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+10x^9+42x^10+52x^11+122x^12+168x^13+210x^14+284x^15+275x^16+276x^17+222x^18+172x^19+102x^20+56x^21+38x^22+4x^23+12x^24+2x^25

The gray image is a code over GF(2) with n=32, k=11 and d=9.
This code was found by Heurico 1.16 in 0.45 seconds.