The generator matrix

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

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+138x^19+3234x^20+2592x^21+13740x^22+16260x^23+72426x^24+54018x^25+145980x^26+141896x^27+54312x^28+22488x^29+3960x^30+264x^31+120x^32+6x^33+6x^36

The gray image is a linear code over GF(3) with n=117, k=12 and d=57.
This code was found by Heurico 1.16 in 76 seconds.