The generator matrix

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

generates a code of length 14 over Z3[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+96x^20+90x^21+318x^22+450x^23+1112x^24+1590x^25+9030x^26+4048x^27+17784x^28+17202x^29+4028x^30+2130x^31+864x^32+166x^33+48x^34+60x^35+28x^36+4x^39

The gray image is a linear code over GF(3) with n=126, k=10 and d=60.
This code was found by Heurico 1.16 in 49.6 seconds.