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

generates a code of length 40 over Z2[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+52x^38+32x^39+93x^40+32x^41+36x^42+9x^44+1x^76

The gray image is a linear code over GF(2) with n=160, k=8 and d=76.
This code was found by Heurico 1.16 in 0.0275 seconds.