The generator matrix

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

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+98x^8+64x^9+272x^10+128x^11+328x^12+64x^13+48x^14+21x^16

The gray image is a linear code over GF(2) with n=44, k=10 and d=16.
This code was found by Heurico 1.16 in 0.51 seconds.