The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^2+16x^3+71x^4+112x^5+56x^6+112x^7+71x^8+16x^9+28x^10+1x^12

The gray image is a code over GF(2) with n=12, k=9 and d=2.
This code was found by Heurico 1.10 in 0 seconds.