The generator matrix

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

generates a code of length 26 over Z5[X]/(X^2) who´s minimum homogenous weight is 103.

Homogenous weight enumerator: w(x)=1x^0+320x^103+200x^104+8x^105+80x^108+16x^110

The gray image is a linear code over GF(5) with n=130, k=4 and d=103.
As d=103 is an upper bound for linear (130,4,5)-codes, this code is optimal over Z5[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.00153 seconds.