The generator matrix

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

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+948x^20+812x^21+5316x^22+4224x^23+23714x^24+20394x^25+47142x^26+46372x^27+20592x^28+5892x^29+1258x^30+246x^31+114x^32+10x^33+4x^36

The gray image is a linear code over GF(3) with n=117, k=11 and d=57.
This code was found by Heurico 1.16 in 7.8 seconds.