The generator matrix

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

generates a code of length 24 over Z5[X]/(X^2) who´s minimum homogenous weight is 95.

Homogenous weight enumerator: w(x)=1x^0+96x^95+500x^96+24x^100+4x^120

The gray image is a linear code over GF(5) with n=120, k=4 and d=95.
As d=95 is an upper bound for linear (120,4,5)-codes, this code is optimal over Z5[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.00124 seconds.