The generator matrix

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

generates a code of length 40 over Z2[X]/(X^4) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+36x^38+54x^39+89x^40+30x^41+28x^42+10x^43+6x^44+2x^53

The gray image is a linear code over GF(2) with n=320, k=8 and d=152.
This code was found by Heurico 1.16 in 0.032 seconds.