The generator matrix

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

generates a code of length 50 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+5x^50+16x^51+6x^52+2x^54+1x^56+1x^58

The gray image is a linear code over GF(2) with n=100, k=5 and d=50.
As d=50 is an upper bound for linear (100,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.0225 seconds.