The generator matrix

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

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+86x^35+747x^36+1332x^37+2238x^38+2432x^39+2978x^40+2398x^41+2126x^42+1092x^43+626x^44+168x^45+98x^46+36x^47+13x^48+4x^49+2x^50+2x^51+3x^52+2x^57

The gray image is a linear code over GF(2) with n=320, k=14 and d=140.
This code was found by Heurico 1.16 in 1.91 seconds.