The generator matrix

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

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+366x^22+198x^23+2056x^24+2058x^25+7020x^26+7506x^27+15228x^28+13878x^29+7576x^30+2730x^31+288x^32+104x^33+30x^34+8x^36+2x^39

The gray image is a linear code over GF(3) with n=126, k=10 and d=66.
This code was found by Heurico 1.16 in 1.03 seconds.