The generator matrix

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

generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+372x^20+162x^21+1788x^22+1962x^23+6828x^24+6840x^25+17856x^26+13400x^27+6876x^28+2598x^29+252x^30+48x^31+54x^32+12x^33

The gray image is a linear code over GF(3) with n=117, k=10 and d=60.
This code was found by Heurico 1.16 in 0.914 seconds.