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.