The generator matrix

 1  0  0  1  1  1  1  1  1  1  1 2X  1  1
 0  1  0  1  0  1  2 2X+1 X+1  0 2X+2  1 2X+1  X
 0  0  1  2  1  1  0 2X  0  1 2X+1  X X+2 2X+2
 0  0  0 2X  0  0 2X 2X  X  X 2X  X  0 2X
 0  0  0  0 2X  X 2X  X  0  X  0  X  X  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+18x^20+114x^21+258x^22+144x^23+332x^24+552x^25+432x^26+736x^27+1170x^28+576x^29+746x^30+804x^31+288x^32+226x^33+132x^34+28x^36+4x^39

The gray image is a linear code over GF(3) with n=42, k=8 and d=20.
This code was found by Heurico 1.16 in 0.848 seconds.