The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+240x^12+542x^16+240x^20+1x^32

The gray image is a code over GF(2) with n=32, k=10 and d=12.
This code was found by Heurico 1.10 in 204 seconds.