The generator matrix

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

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+404x^24+1296x^26+1064x^27+2592x^29+1116x^30+80x^33+6x^36+2x^42

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 1.09 seconds.