The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  X  1  1  1  1  X  X X^2 X^2 X^2  0  0  0  X
 0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0
 0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0

generates a code of length 25 over Z2[X]/(X^3) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+20x^25+3x^26+4x^27+3x^28+1x^30

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^3) for dimension 5.
This code was found by Heurico 1.16 in 0.0035 seconds.