The generator matrix

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

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 0.00169 seconds.