The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1  0 2X
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X+2 2X^2+2X+1  X  1
 0  0 2X^2  0 2X^2 X^2 X^2 X^2  0  0 X^2 2X^2  0
 0  0  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^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+96x^21+216x^22+1348x^24+864x^25+486x^26+2526x^27+864x^28+154x^30+2x^33+2x^36+2x^39

The gray image is a linear code over GF(3) with n=117, k=8 and d=63.
This code was found by Heurico 1.16 in 0.0204 seconds.