The generator matrix

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

generates a code of length 12 over Z2[X]/(X^2) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+60x^7+129x^8+146x^9+222x^10+294x^11+301x^12+324x^13+276x^14+152x^15+78x^16+42x^17+14x^18+6x^19+3x^20

The gray image is a linear code over GF(2) with n=24, k=11 and d=7.
This code was found by Heurico 1.16 in 0.104 seconds.