The generator matrix

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

generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+56x^21+48x^22+116x^24+36x^25+1620x^26+144x^27+54x^28+80x^30+24x^31+4x^33+2x^36+2x^39

The gray image is a linear code over GF(3) with n=117, k=7 and d=63.
This code was found by Heurico 1.16 in 0.00459 seconds.