The generator matrix

 1  0  0  1  1  1  0  X  1 X^2  1  1  X  1 X^2+X  1  X  0  1  1  1  1 X^2+X  1 X^2  1  1  1  1  0 X^2+X  1  1  1  X X^2  1 X^2+X X^2  1  0  1 X^2  1
 0  1  0  0  1  1  1 X^2 X^2+1  1 X^2 X+1  1  X  1  X  1  1 X^2+1  1 X^2+X X+1  1 X^2+1  1 X^2+X+1 X^2  X X^2  1  1 X^2+X X^2 X+1  X  1 X+1  1  1 X^2+1  1 X^2+X+1 X^2  0
 0  0  1  1 X^2 X^2+1  1  1  X X^2+X X^2+X X^2+1 X^2+X+1  1 X^2+1 X^2+X+1 X^2 X+1  X X^2+X+1 X^2  0 X^2+X X^2+1 X^2+X X^2+X  0  1 X^2+X X^2+X+1 X^2+1  X X+1 X^2+X+1  1 X^2+1  1 X^2 X^2  0 X^2  X  1  1
 0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 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 40.

Homogenous weight enumerator: w(x)=1x^0+70x^40+140x^41+214x^42+70x^43+166x^44+92x^45+73x^46+28x^47+66x^48+36x^49+32x^50+14x^51+16x^52+4x^53+1x^54+1x^56

The gray image is a linear code over GF(2) with n=176, k=10 and d=80.
This code was found by Heurico 1.11 in 0.031 seconds.