The generator matrix

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

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+37x^6+174x^8+472x^10+676x^12+482x^14+169x^16+32x^18+4x^20+1x^22

The gray image is a linear code over GF(2) with n=24, k=11 and d=6.
This code was found by Heurico 1.16 in 0.0177 seconds.