The generator matrix

 1  1  1  1  1  1  1  X  1  X  X
 0  X  0 X^2+X  0  0  0 X^2+X X^2 X^2+X X^2
 0  0 X^2  0  0  0  0 X^2 X^2 X^2  0
 0  0  0 X^2  0  0 X^2 X^2  0  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 X^2 X^2 X^2 X^2

generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+66x^8+32x^9+48x^10+192x^11+104x^12+32x^13+16x^14+21x^16

The gray image is a linear code over GF(2) with n=44, k=9 and d=16.
This code was found by Heurico 1.16 in 0.0844 seconds.