The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  X  1  1
 0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0
 0  0 X^2  0  0  0 X^2 2X^2 2X^2 X^2 X^2  0  0  0
 0  0  0 X^2  0  0 2X^2 2X^2 X^2  0 X^2 2X^2  0  0
 0  0  0  0 X^2  0 2X^2 X^2 2X^2 X^2  0 2X^2  0  0
 0  0  0  0  0 X^2 X^2  0 X^2 X^2 2X^2 2X^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+132x^18+54x^22+132x^24+324x^25+110x^27+5022x^28+432x^31+330x^33+24x^42

The gray image is a linear code over GF(3) with n=126, k=8 and d=54.
This code was found by Heurico 1.16 in 0.0329 seconds.