The generator matrix

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

generates a code of length 19 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+114x^36+108x^39+18x^45+2x^54

The gray image is a linear code over GF(3) with n=57, k=5 and d=36.
As d=36 is an upper bound for linear (57,5,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.00139 seconds.