The generator matrix

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

generates a code of length 14 over Z3[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+6x^16+290x^18+72x^19+162x^20+1236x^21+684x^22+1296x^23+5170x^24+2904x^25+3888x^26+10948x^27+5328x^28+5184x^29+11130x^30+3744x^31+2592x^32+3820x^33+384x^34+182x^36+28x^42

The gray image is a linear code over GF(3) with n=42, k=10 and d=16.
This code was found by Heurico 1.16 in 47.4 seconds.