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.