The generator matrix

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

generates a code of length 14 over Z3[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+168x^22+54x^23+786x^24+786x^25+2268x^26+2576x^27+4788x^28+4374x^29+2610x^30+1002x^31+108x^32+96x^33+60x^34+6x^36

The gray image is a linear code over GF(3) with n=126, k=9 and d=66.
This code was found by Heurico 1.16 in 0.159 seconds.