The generator matrix

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

generates a code of length 40 over Z2[X]/(X^3) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+228x^35+308x^36+486x^37+446x^38+504x^39+386x^40+466x^41+332x^42+336x^43+228x^44+194x^45+70x^46+80x^47+21x^48+6x^49+4x^51

The gray image is a linear code over GF(2) with n=160, k=12 and d=70.
This code was found by Heurico 1.11 in 0.172 seconds.