The generator matrix

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

generates a code of length 13 over Z3[X]/(X^3) who�s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+132x^18+54x^20+132x^21+324x^23+5022x^26+110x^27+432x^29+330x^30+24x^39

The gray image is a linear code over GF(3) with n=117, k=8 and d=54.
This code was found by Heurico 1.16 in 0.0328 seconds.