The generator matrix

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

generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+120x^18+330x^21+324x^22+3894x^24+1296x^25+4374x^26+7358x^27+1296x^28+588x^30+102x^33

The gray image is a linear code over GF(3) with n=117, k=9 and d=54.
This code was found by Heurico 1.16 in 0.118 seconds.