The generator matrix

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

generates a code of length 20 over Z5[X]/(X^2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+400x^79+120x^80+100x^84+4x^100

The gray image is a linear code over GF(5) with n=100, k=4 and d=79.
As d=79 is an upper bound for linear (100,4,5)-codes, this code is optimal over Z5[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000793 seconds.