The generator matrix

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

generates a code of length 18 over Z3[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+108x^24+162x^27+226x^30+358x^33+1458x^34+13504x^36+2916x^37+466x^39+274x^42+130x^45+64x^48+16x^51

The gray image is a linear code over GF(3) with n=162, k=9 and d=72.
This code was found by Heurico 1.16 in 0.438 seconds.