The generator matrix

 1  0  0  1  1  1
 0  1  0  1  0  0
 0  0  1  1  0  0
 0  0  0  X  0  0
 0  0  0  0  X  0

generates a code of length 6 over Z2[X]/(X^2) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+16x^2+55x^4+112x^6+55x^8+16x^10+1x^12

The gray image is a linear code over GF(2) with n=12, k=8 and d=2.
This code was found by Heurico 1.16 in 0.000103 seconds.