The generator matrix

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

generates a code of length 5 over Z3[X]/(X^3) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+14x^9+54x^10+12x^12

The gray image is a linear code over GF(3) with n=45, k=4 and d=27.
As d=29 is an upper bound for linear (45,4,3)-codes, this code is optimal over Z3[X]/(X^3) for dimension 4.
This code was found by Heurico 1.16 in 5.51e-005 seconds.