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.