The generator matrix

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

generates a code of length 12 over Z2[X]/(X^2) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+44x^5+165x^6+338x^7+673x^8+1276x^9+1925x^10+2462x^11+2679x^12+2376x^13+1879x^14+1326x^15+730x^16+332x^17+127x^18+34x^19+13x^20+4x^21

The gray image is a linear code over GF(2) with n=24, k=14 and d=5.
This code was found by Heurico 1.16 in 1.44 seconds.