The generator matrix

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

generates a code of length 18 over Z3[X]/(X^2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+84x^31+36x^33+156x^34+186x^36+108x^37+114x^40+18x^42+24x^43+2x^54

The gray image is a linear code over GF(3) with n=54, k=6 and d=31.
This code was found by Heurico 1.16 in 0.805 seconds.