The generator matrix

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

generates a code of length 12 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+84x^4+272x^6+1063x^8+1648x^10+2056x^12+1648x^14+1063x^16+272x^18+84x^20+1x^24

The gray image is a linear code over GF(2) with n=24, k=13 and d=4.
This code was found by Heurico 1.16 in 0.121 seconds.