The generator matrix

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

generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+88x^15+172x^18+226x^21+1966x^24+13122x^26+3396x^27+412x^30+214x^33+76x^36+10x^39

The gray image is a linear code over GF(3) with n=117, k=9 and d=45.
This code was found by Heurico 1.16 in 0.183 seconds.