The generator matrix

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

generates a code of length 18 over Z5[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+360x^70+264x^75

The gray image is a linear code over GF(5) with n=90, k=4 and d=70.
As d=70 is an upper bound for linear (90,4,5)-codes, this code is optimal over Z5[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000632 seconds.