The generator matrix

 1  0  0  0  1  1  1  1 X^2  1 X^2+X  X  0  1  1  1  1 X^2  1 X^2+X  0  1 X^2+X X^2+X X^2  1  0  X  1  X  1 X^2+X X^2+X  1  1 X^2  0  1  1 X^2
 0  1  0  0  0 X^2 X^2+1  1  1 X^2+1  1  1 X^2+X  X X+1 X^2+X  1  1 X^2  X  1 X+1  0  1  0  X X^2  1 X^2+1  1  1  1 X^2 X^2+X  0  1 X^2+X  X X^2+X+1 X^2
 0  0  1  0 X^2  1 X^2 X^2+1 X+1  X X^2+X X^2+1  1  1 X^2+X+1 X^2 X^2+X+1  X X^2 X^2  1  0  1 X+1  1 X+1 X^2+X X^2+X  0 X^2 X^2+X X+1  1 X^2+X  X X^2+X+1 X^2+X  1  0  0
 0  0  0  1 X^2+X+1 X^2+X+1 X+1  X X+1 X^2+X X^2+1 X^2 X+1  0 X^2+X+1 X^2+1 X^2  1 X^2+X  1 X^2+X X+1  0  X X+1 X^2  1  X X^2+X  0  1  0  1  X  1 X^2+1  1 X^2+1  X  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+206x^35+361x^36+420x^37+532x^38+460x^39+386x^40+390x^41+407x^42+334x^43+249x^44+168x^45+82x^46+56x^47+27x^48+14x^49+3x^50

The gray image is a linear code over GF(2) with n=160, k=12 and d=70.
This code was found by Heurico 1.16 in 0.351 seconds.