The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2  X  1 X^2  X  X  0  1 X^2  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^2 X^3 X^3 X^2 X^3+X^2  0  0 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3  0  0 X^2 X^2 X^3  0 X^3+X^2 X^3  0
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^2 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^3  0 X^3+X^2 X^3+X^2  0  0  0 X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^2 X^2 X^2 X^3+X^2
 0  0  0 X^3  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3
 0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3
 0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0  0  0

generates a code of length 40 over Z2[X]/(X^4) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+56x^35+96x^36+138x^37+224x^38+332x^39+380x^40+340x^41+224x^42+104x^43+96x^44+28x^45+12x^47+2x^48+4x^49+8x^51+2x^53+1x^64

The gray image is a linear code over GF(2) with n=320, k=11 and d=140.
This code was found by Heurico 1.16 in 142 seconds.