The generator matrix

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

generates a code of length 13 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+130x^18+216x^19+654x^20+726x^21+630x^22+1524x^23+1824x^24+1512x^25+3978x^26+2484x^27+1512x^28+2352x^29+1320x^30+504x^31+240x^32+66x^33+4x^36+6x^39

The gray image is a linear code over GF(3) with n=39, k=9 and d=18.
This code was found by Heurico 1.16 in 0.703 seconds.