The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  X  1
 0  X  0 2X^2+X 2X  0  X 2X^2+2X 2X X^2 X^2 2X 2X^2 2X^2+X
 0  0  X X^2+2X  0 2X  X 2X^2+X 2X 2X^2 2X^2+2X X^2 2X  0
 0  0  0 X^2 X^2 X^2  0 X^2 2X^2 2X^2 X^2  0  0 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+72x^22+144x^23+206x^24+258x^25+216x^26+738x^27+3222x^28+432x^29+744x^30+270x^31+180x^32+4x^33+66x^34+2x^36+6x^39

The gray image is a linear code over GF(3) with n=126, k=8 and d=66.
This code was found by Heurico 1.16 in 0.0366 seconds.