The generator matrix

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

generates a code of length 6 over Z4 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+6x^2+15x^4+84x^6+15x^8+6x^10+1x^12

The gray image is a code over GF(2) with n=12, k=7 and d=2.
This code was found by Heurico 1.16 in 9.68e-005 seconds.