The generator matrix

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

generates a code of length 14 over Z3[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+426x^24+240x^25+402x^26+1304x^27+1806x^28+708x^29+1372x^30+204x^31+24x^32+54x^33+18x^34+2x^39

The gray image is a linear code over GF(3) with n=126, k=8 and d=72.
This code was found by Heurico 1.16 in 1.94 seconds.