The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1 X^2  1  1  1  1  1  1  1  1  0
 0  X  0  X  0  0 X^2+X X^2+X X^2+X  0 X^2 X^2+X  0 X^2  X  X X^2+X X^2 X^2  X  X X^2 X^2+X X^2 X^2+X X^2  0  X  X X^2+X X^2  X  0 X^2+X  0  0 X^2+X X^2  X  0  X X^2 X^2+X  0
 0  0  X  X  0 X^2+X X^2+X  0  0 X^2  X X^2+X  0  X X^2+X X^2 X^2 X^2  X X^2+X  0  0  0 X^2+X X^2+X  0  X X^2+X X^2 X^2  0  0  X  X X^2  0 X^2  X  X X^2  X X^2+X X^2  X
 0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0  0
 0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0 X^2  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+28x^40+36x^41+42x^42+144x^43+92x^44+40x^45+84x^46+16x^47+6x^48+4x^49+2x^50+16x^53+1x^80

The gray image is a linear code over GF(2) with n=176, k=9 and d=80.
This code was found by Heurico 1.16 in 0.048 seconds.