The generator matrix

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

generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+76x^41+110x^42+80x^43+46x^44+48x^45+80x^46+24x^47+15x^48+16x^49+2x^50+8x^51+1x^52+4x^57+1x^68

The gray image is a linear code over GF(2) with n=176, k=9 and d=82.
This code was found by Heurico 1.16 in 0.0438 seconds.