The generator matrix

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

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+550x^35+1099x^36+3100x^37+3492x^38+5606x^39+4972x^40+6130x^41+3415x^42+2630x^43+1023x^44+560x^45+66x^46+90x^47+9x^48+18x^49+3x^50+4x^51

The gray image is a linear code over GF(2) with n=320, k=15 and d=140.
This code was found by Heurico 1.16 in 585 seconds.