The generator matrix

 1  1  1  1  1  1  X  1  1  X  1  X  1  1
 0  X 2X  0 2X^2+X 2X 2X^2+X  0 2X^2+X 2X 2X 2X^2+X  0  0
 0  0 X^2  0  0  0 2X^2  0 X^2 2X^2 X^2 X^2  0  0
 0  0  0 X^2  0  0 2X^2 X^2 2X^2  0 2X^2 X^2  0  0
 0  0  0  0 2X^2  0 2X^2 2X^2 2X^2 2X^2  0 2X^2  0  0
 0  0  0  0  0 X^2  0 2X^2 2X^2 X^2 X^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+162x^22+834x^24+972x^25+1458x^26+2162x^27+6318x^28+2916x^29+2376x^30+1296x^31+762x^33+24x^42

The gray image is a linear code over GF(3) with n=126, k=9 and d=54.
This code was found by Heurico 1.16 in 0.203 seconds.