The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1 X X X 1 1 X X^2 X^2 X^2 1 X X X X X X X X X X^2
0 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0
0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 0 0 0
generates a code of length 40 over Z2[X]/(X^4) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+57x^40+4x^44+2x^52
The gray image is a linear code over GF(2) with n=320, k=6 and d=160.
This code was found by Heurico 1.16 in 0.016 seconds.