The generator matrix

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

generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+108x^20+108x^21+552x^22+528x^23+2612x^24+1584x^25+6408x^26+5148x^27+1656x^28+720x^29+138x^30+96x^31+12x^32+10x^33+2x^36

The gray image is a linear code over GF(3) with n=117, k=9 and d=60.
This code was found by Heurico 1.16 in 0.143 seconds.