The generator matrix

 1  1  1  1  1  1  X  1  1  X  1  X  1
 0  X 2X  0 2X^2+X 2X 2X^2+X  0 2X^2+X 2X 2X 2X^2+X  0
 0  0 X^2  0  0  0 2X^2  0 X^2 2X^2 X^2 X^2  0
 0  0  0 X^2  0  0 2X^2 X^2 2X^2  0 2X^2 X^2  0
 0  0  0  0 2X^2  0 2X^2 2X^2 2X^2 2X^2  0 2X^2  0
 0  0  0  0  0 X^2  0 2X^2 2X^2 X^2 X^2 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+186x^18+162x^20+348x^21+486x^22+972x^23+1782x^24+1944x^25+6318x^26+3458x^27+1944x^28+1296x^29+762x^30+24x^39

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 0.202 seconds.