The generator matrix
1 0 0 0 1 1 1 0 1 1 1 1
0 1 0 0 0 1 1 1 X X 0 0
0 0 1 0 1 1 0 1 0 X X 0
0 0 0 1 1 0 1 1 1 X+1 1 0
0 0 0 0 X 0 0 X 0 0 X 0
0 0 0 0 0 X 0 X X X X 0
0 0 0 0 0 0 X X X 0 X 0
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+39x^6+68x^7+87x^8+148x^9+219x^10+296x^11+337x^12+296x^13+213x^14+148x^15+84x^16+68x^17+41x^18+3x^20
The gray image is a linear code over GF(2) with n=24, k=11 and d=6.
This code was found by Heurico 1.16 in 0.0128 seconds.