The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+13x^12+1x^16+1x^20

The gray image is a code over GF(2) with n=24, k=4 and d=12.
This code was found by Heurico 1.16 in 0.00023 seconds.