The generator matrix

 1  0  1  1  1  1
 0  1  1  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+10x^2+31x^4+64x^5+44x^6+64x^7+31x^8+10x^10+1x^12

The gray image is a code over GF(2) with n=12, k=8 and d=2.
This code was found by Heurico 1.16 in 0.000171 seconds.