The generator matrix

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

generates a code of length 13 over Z3[X]/(X^3) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+108x^19+318x^20+344x^21+1554x^22+1272x^23+7784x^24+5598x^25+18468x^26+15484x^27+5580x^28+1716x^29+430x^30+282x^31+96x^32+10x^33+4x^36

The gray image is a linear code over GF(3) with n=117, k=10 and d=57.
This code was found by Heurico 1.16 in 1.1 seconds.