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  1  1  1  1  1  1  1  1  1  1
 0 X^3  0  0  0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3
 0  0 X^3  0  0  0  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 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 X^3 X^3
 0  0  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3  0  0  0  0  0 X^3 X^3  0  0  0
 0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0  0  0
 0  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  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+16x^36+478x^40+16x^44+1x^80

The gray image is a linear code over GF(2) with n=320, k=9 and d=144.
This code was found by Heurico 1.16 in 0.032 seconds.