The generator matrix

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

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+344x^40+558x^42+493x^44+300x^46+164x^48+126x^50+51x^52+8x^54+3x^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 0.379 seconds.