The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 X 0 X 0 X 2X 2X 2X 0 0 X X 0 X 2X 2X 2X
0 0 X 2X 2X X 0 X 2X 0 X 2X X 2X 0 0 X 2X
generates a code of length 18 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+78x^36+2x^54
The gray image is a linear code over GF(3) with n=54, k=4 and d=36.
As d=36 is an upper bound for linear (54,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000722 seconds.