The generator matrix

1 0 0 0 0 1
0 1 0 0 0 1
0 0 1 0 0 1
0 0 0 1 0 1
0 0 0 0 1 1

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

Homogenous weight enumerator: w(x)=1x^0+30x^2+255x^4+452x^6+255x^8+30x^10+1x^12

The gray image is a code over GF(2) with n=12, k=10 and d=2.
This code was found by Heurico 1.10 in 0 seconds.