The generator matrix

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

generates a code of length 16 over Z4 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+12x^12+16x^13+7x^14+16x^15+19x^16+16x^17+20x^18+16x^19+4x^22+1x^30

The gray image is a code over GF(2) with n=32, k=7 and d=12.
This code was found by Heurico 1.16 in 0.000952 seconds.