The generator matrix

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

generates a code of length 6 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+3x^4+8x^6+3x^8+1x^12

The gray image is a linear code over GF(2) with n=12, k=4 and d=4.
This code was found by Heurico 1.16 in 5.58e-005 seconds.