The generator matrix

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

generates a code of length 14 over Z3[X]/(X^3) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+58x^21+54x^22+138x^24+324x^25+1458x^26+188x^27+648x^28+2916x^29+220x^30+432x^31+96x^33+18x^36+10x^39

The gray image is a linear code over GF(3) with n=126, k=8 and d=63.
This code was found by Heurico 1.16 in 0.212 seconds.