The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^12+3x^16

The gray image is a code over GF(2) with n=24, k=5 and d=12.
This code was found by Heurico 1.16 in 0.000326 seconds.