The generator matrix

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

generates a code of length 14 over Z3[X]/(X^2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+78x^19+126x^20+236x^21+594x^22+528x^23+962x^24+1902x^25+1092x^26+2318x^27+3234x^28+1692x^29+2492x^30+2556x^31+804x^32+530x^33+384x^34+132x^35+12x^36+8x^39+2x^42

The gray image is a linear code over GF(3) with n=42, k=9 and d=19.
This code was found by Heurico 1.16 in 0.54 seconds.