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

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+9x^38+54x^39+141x^40+32x^41+6x^42+8x^43+2x^44+1x^46+2x^55

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 0.047 seconds.