The generator matrix

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

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+159x^6+350x^7+680x^8+1250x^9+1946x^10+2446x^11+2646x^12+2458x^13+1872x^14+1258x^15+759x^16+342x^17+118x^18+42x^19+10x^20+2x^21+1x^22

The gray image is a linear code over GF(2) with n=24, k=14 and d=5.
This code was found by Heurico 1.10 in 0.109 seconds.