The generator matrix

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

generates a code of length 14 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+216x^18+84x^19+510x^20+940x^21+624x^22+2418x^23+3032x^24+2496x^25+7908x^26+6368x^27+6396x^28+10128x^29+6346x^30+3048x^31+5034x^32+2576x^33+474x^34+246x^35+192x^36+4x^39+8x^42

The gray image is a linear code over GF(3) with n=42, k=10 and d=18.
This code was found by Heurico 1.16 in 4.25 seconds.