The generator matrix

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

generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+90x^22+54x^23+282x^24+90x^25+1026x^26+402x^27+90x^28+54x^29+42x^30+54x^31+2x^36

The gray image is a linear code over GF(3) with n=117, k=7 and d=66.
This code was found by Heurico 1.16 in 0.0043 seconds.