The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+192x^12+168x^14+321x^16+144x^18+184x^20+8x^22+6x^24

The gray image is a code over GF(2) with n=32, k=10 and d=12.
This code was found by Heurico 1.16 in 14.1 seconds.