The generator matrix

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

generates a code of length 23 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+54x^45+18x^48+8x^54

The gray image is a linear code over GF(3) with n=69, k=4 and d=45.
As d=45 is an upper bound for linear (69,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.00184 seconds.