The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+73x^12+136x^14+116x^16+96x^18+79x^20+8x^22+3x^24

The gray image is a code over GF(2) with n=32, k=9 and d=12.
This code was found by Heurico 1.16 in 0.00571 seconds.