The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1
 0  2  0  0  0  0  0  2  0  2  2  0  0  2  2  0
 0  0  2  0  0  0  2  2  0  2  0  0  2  2  0  0
 0  0  0  2  0  0  2  0  0  2  2  2  2  0  0  0
 0  0  0  0  2  0  2  0  2  2  0  2  0  2  0  0
 0  0  0  0  0  2  2  0  2  0  2  0  0  2  2  0

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

Homogenous weight enumerator: w(x)=1x^0+16x^12+11x^14+32x^15+11x^16+32x^17+12x^18+4x^20+8x^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 0.00141 seconds.