The generator matrix

 1  0  1  X  1  1  1  1  1  1  1 2X  1  1  1 4X  1  1  1 3X  1  1  1  1  1
 0  1  X  1 3X+1 4X+1  2 X+2 2X 2X+1 2X+2  1 4X X+1 4X+2  1 3X  1 3X+2  1 3X+4 4X+4 2X+4 X+4  4

generates a code of length 25 over Z5[X]/(X^2) who´s minimum homogenous weight is 100.

Homogenous weight enumerator: w(x)=1x^0+620x^100+4x^125

The gray image is a linear code over GF(5) with n=125, k=4 and d=100.
As d=100 is an upper bound for linear (125,4,5)-codes, this code is optimal over Z5[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.00134 seconds.