The generator matrix

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

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+72x^18+24x^19+156x^20+288x^21+240x^22+714x^23+1152x^24+960x^25+2658x^26+1940x^27+1758x^28+3678x^29+2178x^30+1272x^31+1446x^32+846x^33+120x^34+96x^35+66x^36+18x^39

The gray image is a linear code over GF(3) with n=42, k=9 and d=18.
This code was found by Heurico 1.16 in 0.423 seconds.