The generator matrix

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

generates a code of length 26 over Z3[X]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+52x^51+162x^52+26x^54+2x^78

The gray image is a linear code over GF(3) with n=78, k=5 and d=51.
As d=51 is an upper bound for linear (78,5,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 15.6 seconds.