The generator matrix

 1  0  0  1  1  1  0 X^2  1  1 X^2  1 X^2+X  1  X  1  1  0  1  1  X  1  1  X  1  1 X^2  1 X^2+X  1  1  1  1  1  X  1  1  1 X^2 X^2  X  1 X^2+X  1
 0  1  0  0 X^2+1 X^2+1  1  X X^2  1  1 X^2+X  1 X+1  X  X  X  1  1 X^2+X+1  1 X^2 X^2+X+1  1  X X^2+X+1  0 X^2+X  1 X^2  0 X^2+X  1  0  1 X^2+X+1 X^2+X X^2  1  1  1 X^2+X+1  1 X^2
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1  X X^2+1  1  1  0 X^2  1 X^2+X X+1 X^2+X  1 X^2 X^2+1 X^2+1 X^2+X X^2+X+1  0  1  1 X^2+1 X^2+1 X^2+X+1  0 X^2+X X+1 X^2+X  0 X^2+X+1 X+1 X^2+1 X^2 X^2+X X+1 X^2+1  1  X
 0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0  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+60x^40+150x^41+181x^42+166x^43+117x^44+72x^45+45x^46+64x^47+65x^48+34x^49+28x^50+26x^51+13x^52+1x^54+1x^58

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 0.0541 seconds.