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^2  1  1  1  1  1  1  1  X  X  X
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2  0 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3 X^3+X^2 X^2  0  0 X^3 X^3+X^2 X^2  0  0 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^2 X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2
 0  0 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0  0  0 X^3 X^3
 0  0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3
 0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0  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+69x^36+104x^38+626x^40+128x^41+32x^42+39x^44+24x^46+1x^72

The gray image is a linear code over GF(2) with n=320, k=10 and d=144.
This code was found by Heurico 1.16 in 0.062 seconds.