The generator matrix

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

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+93x^4+298x^6+128x^7+1106x^8+1152x^9+1624x^10+2816x^11+1906x^12+2816x^13+1756x^14+1152x^15+941x^16+128x^17+408x^18+49x^20+10x^22

The gray image is a linear code over GF(2) with n=24, k=14 and d=4.
This code was found by Heurico 1.16 in 0.829 seconds.