The generator matrix

 1  0  0  1  1  1  2  1  1  0  1  1  2  0  1  1
 0  1  0  1  0  3  1  0  1  1  3  3  1  1  2  0
 0  0  1  1  1  0  1  0  3  2  1  2  1  3  2  0
 0  0  0  2  0  2  0  2  0  2  0  2  2  0  2  0
 0  0  0  0  2  0  0  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+35x^12+72x^14+56x^16+48x^18+33x^20+8x^22+3x^24

The gray image is a code over GF(2) with n=32, k=8 and d=12.
This code was found by Heurico 1.16 in 0.00187 seconds.