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
 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

generates a code of length 22 over Z5[X]/(X^2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+120x^86+320x^87+16x^90+80x^91+80x^92+8x^95

The gray image is a linear code over GF(5) with n=110, k=4 and d=86.
As d=86 is an upper bound for linear (110,4,5)-codes, this code is optimal over Z5[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.00101 seconds.