The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1
 0  1  0  0  0  1  1  1  X  X  0  0
 0  0  1  0  1  1  0  1  0  0  1  1
 0  0  0  1  1  0  1  1  1 X+1  1  1
 0  0  0  0  X  0  0  0  0  X  X  X
 0  0  0  0  0  X  0  0  X  0  X  X
 0  0  0  0  0  0  X  0  X  X  X  0
 0  0  0  0  0  0  0  X  X  0  X  0

generates a code of length 12 over Z2[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+79x^6+348x^8+938x^10+1354x^12+960x^14+339x^16+70x^18+6x^20+1x^22

The gray image is a linear code over GF(2) with n=24, k=12 and d=6.
This code was found by Heurico 1.16 in 0.0494 seconds.