The generator matrix

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

generates a code of length 40 over Z2[X]/(X^3) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+34x^34+106x^35+153x^36+196x^37+230x^38+220x^39+234x^40+228x^41+193x^42+170x^43+110x^44+78x^45+45x^46+16x^47+13x^48+8x^49+9x^50+1x^52+2x^53+1x^54

The gray image is a linear code over GF(2) with n=160, k=11 and d=68.
This code was found by Heurico 1.16 in 0.139 seconds.