The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+220x^12+64x^14+461x^16+64x^18+204x^20+10x^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 9.85 seconds.