The generator matrix

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

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+400x^40+464x^42+494x^44+296x^46+267x^48+64x^50+50x^52+8x^54+4x^56

The gray image is a linear code over GF(2) with n=176, k=11 and d=80.
This code was found by Heurico 1.16 in 35.7 seconds.