The generator matrix
1 0 1 1 1 0 1 1 0 1 1 1
0 1 1 0 1 1 0 1 1 0 0 X+1
0 0 X 0 0 0 0 0 0 X X 0
0 0 0 X 0 0 0 0 X X X 0
0 0 0 0 X 0 0 0 X 0 0 X
0 0 0 0 0 X 0 0 X 0 X X
0 0 0 0 0 0 X 0 X X 0 0
0 0 0 0 0 0 0 X 0 X X X
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+17x^6+8x^7+54x^8+72x^9+108x^10+176x^11+148x^12+176x^13+118x^14+72x^15+49x^16+8x^17+12x^18+4x^20+1x^22
The gray image is a linear code over GF(2) with n=24, k=10 and d=6.
This code was found by Heurico 1.16 in 0.0059 seconds.