The generator matrix

 1  1  1  1  1  1  1  1  2  2  2  2
 0  2  0  2  0  0  2  2  0  2  2  0
 0  0  2  2  0  2  2  0  2  2  0  0

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

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

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 0.00028 seconds.