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

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+43x^36+142x^38+128x^39+436x^40+128x^41+94x^42+25x^44+18x^46+6x^48+2x^50+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 0.063 seconds.