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.