The generator matrix

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

generates a code of length 6 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+12x^6+3x^8

The gray image is a code over GF(2) with n=12, k=4 and d=6.
This code was found by Heurico 1.16 in 7.8e-005 seconds.