The generator matrix

 1  0  1  1  1  0  1  1  X  1  1  X  1  1  0  1  1  0  1  1  1  1  X  X  X  X  0  0  1  1  1  1  0  X  X  X  0  X  X  X
 0  1  1  0 X+1  1  X X+1  1  X  1  1  0 X+1  1  0 X+1  1  X  X  1  1  1  1  0  X  X  0  0  X X+1  1  1  1  0  X  X  0  X  0
 0  0  X  X  0  X  X  X  X  0  0  0  0  0  X  X  X  0  X  0  X  0  X  0  X  X  X  X  0  0  0  0  X  X  0  0  0  X  X  0

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+18x^40+8x^42+4x^44+1x^48

The gray image is a linear code over GF(2) with n=80, k=5 and d=40.
As d=40 is an upper bound for linear (80,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.00674 seconds.