The generator matrix

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

generates a code of length 40 over Z2[X]/(X^4) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+265x^36+680x^37+1387x^38+1200x^39+1606x^40+982x^41+975x^42+542x^43+373x^44+94x^45+49x^46+18x^47+11x^48+4x^49+5x^50

The gray image is a linear code over GF(2) with n=320, k=13 and d=144.
This code was found by Heurico 1.16 in 0.796 seconds.