The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  X  1  1  0  X X^2  1  X  1  X  1  1 X^2  1
 0  X  0  X  0  0  X X^2+X X^2 X^2  X X^2+X X^2  X  X  0  X X^2  0 X^2+X X^2+X  0  0 X^2+X  0 X^2+X X^2 X^2  0 X^2+X X^2  0  X  0  X  X  X  X X^2+X X^2  X X^2+X  X X^2+X
 0  0  X  X  0 X^2+X  X X^2  0  X  X  0  X X^2+X  0 X^2  X X^2+X X^2  0  X X^2+X  0 X^2  0 X^2  0  X  X X^2  X X^2+X  X  X X^2+X  X X^2+X X^2+X  X  X X^2+X  X  X X^2+X
 0  0  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0  0  0  0 X^2
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0  0  0 X^2  0
 0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  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+246x^40+128x^42+304x^44+128x^46+199x^48+17x^56+1x^72

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 22.4 seconds.