The generator matrix

 1  0  0  0  0  1  1  1  1  0  1  1
 0  1  0  0  0  0  0  1  1  1  X  X
 0  0  1  0  0  0  1  0  1 X+1  X  0
 0  0  0  1  0  1  1 X+1  0 X+1 X+1  0
 0  0  0  0  1  1  0  X  0  X  0  1
 0  0  0  0  0  X  0  0  X  X  X  0
 0  0  0  0  0  0  X  X  X  X  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+52x^6+100x^7+158x^8+264x^9+508x^10+700x^11+644x^12+560x^13+428x^14+348x^15+217x^16+72x^17+36x^18+4x^19+4x^20

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 0.0564 seconds.