The generator matrix

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

generates a code of length 14 over Z3[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+240x^20+320x^21+360x^22+924x^23+866x^24+720x^25+2436x^26+2420x^27+1998x^28+3216x^29+2246x^30+1152x^31+1776x^32+680x^33+144x^34+156x^35+18x^36+8x^39+2x^42

The gray image is a linear code over GF(3) with n=42, k=9 and d=20.
This code was found by Heurico 1.16 in 58.3 seconds.