The generator matrix

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

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+42x^21+546x^22+300x^23+1558x^24+1410x^25+8604x^26+5238x^27+16092x^28+16884x^29+5338x^30+2226x^31+456x^32+206x^33+138x^34+8x^36+2x^39

The gray image is a linear code over GF(3) with n=126, k=10 and d=63.
This code was found by Heurico 1.16 in 1.27 seconds.