The generator matrix
1 0 1 1 1 0 X 1 1 X 1
0 1 1 0 X+1 1 X 0 X X 0
0 0 X 0 X 0 0 X X^2 X 0
0 0 0 X X X^2+X X X X^2+X 0 X^2
0 0 0 0 X^2 0 X^2 0 X^2 0 X^2
0 0 0 0 0 X^2 X^2 0 0 X^2 0
generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+26x^6+82x^7+229x^8+442x^9+758x^10+996x^11+795x^12+452x^13+206x^14+74x^15+30x^16+2x^17+2x^18+1x^20
The gray image is a linear code over GF(2) with n=44, k=12 and d=12.
This code was found by Heurico 1.16 in 0.0225 seconds.