The generator matrix

 1  1  1  1  1  1  X  1  X  1  1  1  1
 0  X 2X  0 2X^2+X 2X 2X^2+X  0 2X  0 X^2 X^2  0
 0  0 X^2  0  0 X^2 2X^2 X^2  0 X^2 2X^2 2X^2  0
 0  0  0 X^2  0 2X^2 X^2 X^2 2X^2  0 2X^2 2X^2  0
 0  0  0  0 2X^2 2X^2 2X^2  0 2X^2 X^2 X^2 2X^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+66x^18+120x^21+162x^22+1116x^24+648x^25+1458x^26+2102x^27+648x^28+132x^30+108x^33

The gray image is a linear code over GF(3) with n=117, k=8 and d=54.
This code was found by Heurico 1.16 in 0.0263 seconds.