The generator matrix

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

generates a code of length 40 over Z2[X]/(X^3) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+226x^31+729x^32+1604x^33+3099x^34+4752x^35+7916x^36+9628x^37+13870x^38+14016x^39+17915x^40+15062x^41+14788x^42+10044x^43+7758x^44+4412x^45+2786x^46+1374x^47+602x^48+260x^49+145x^50+52x^51+22x^52+8x^53+1x^56+2x^57

The gray image is a linear code over GF(2) with n=160, k=17 and d=62.
This code was found by Heurico 1.13 in 107 seconds.