The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1 2X  1  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

generates a code of length 21 over Z5[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+180x^82+240x^83+12x^85+120x^87+60x^88+12x^90

The gray image is a linear code over GF(5) with n=105, k=4 and d=82.
As d=82 is an upper bound for linear (105,4,5)-codes, this code is optimal over Z5[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000893 seconds.