The generator matrix

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

generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+226x^40+160x^42+282x^44+144x^46+177x^48+16x^50+14x^52+3x^56+1x^72

The gray image is a linear code over GF(2) with n=176, k=10 and d=80.
This code was found by Heurico 1.16 in 0.691 seconds.