The generator matrix

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

generates a code of length 14 over Z3[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+186x^18+216x^21+1620x^22+1320x^24+972x^25+10206x^26+4106x^27+10692x^28+20412x^29+4320x^30+4212x^31+762x^33+24x^42

The gray image is a linear code over GF(3) with n=126, k=10 and d=54.
This code was found by Heurico 1.16 in 0.885 seconds.