The generator matrix

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

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+22x^25+3x^26+3x^28+2x^29+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 0.00527 seconds.