The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  0  X  0  0  0
 0  X  0  0  0  X  X  X  0  0  0  0  X  X  X  X  X  X  X  X
 0  0  X  0  X  X  X  0  0  0  X  X  X  X  0  0  0  0  X  X
 0  0  0  X  X  0  X  X  0  X  X  0  0  X  X  0  0  X  X  0

generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+28x^20+2x^24+1x^32

The gray image is a linear code over GF(2) with n=40, k=5 and d=20.
As d=20 is an upper bound for linear (40,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.0025 seconds.