The generator matrix

 1  0  1  1  1 X^2+X  1  1  1  1  0
 0  1  1 X^2+X X^2+X+1  1 X^2  X X+1  0  1
 0  0  X  0 X^2+X X^2  X X^2+X  0  0 X^2
 0  0  0 X^2  0 X^2  0 X^2  0 X^2  0
 0  0  0  0 X^2  0 X^2  0 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+72x^8+96x^9+248x^10+192x^11+252x^12+96x^13+56x^14+11x^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 0.00668 seconds.