The generator matrix
1 1 1 1 1 1 X X X
0 X^2 2X^2 0 X^2 2X^2 X^2 2X^2 0
generates a code of length 9 over Z3[X]/(X^3) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+74x^18+6x^21
The gray image is a linear code over GF(3) with n=81, k=4 and d=54.
As d=54 is an upper bound for linear (81,4,3)-codes, this code is optimal over Z3[X]/(X^3) for dimension 4.
This code was found by Heurico 1.16 in 0.000155 seconds.