The generator matrix

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

generates a code of length 40 over Z2[X]/(X^3) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+24x^37+54x^38+86x^40+32x^41+40x^42+8x^44+8x^45+1x^46+1x^48+1x^62

The gray image is a linear code over GF(2) with n=160, k=8 and d=74.
This code was found by Heurico 1.16 in 7.22 seconds.