The generator matrix

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

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+100x^21+1218x^22+774x^23+5552x^24+5814x^25+22008x^26+21370x^27+46098x^28+43110x^29+21606x^30+7962x^31+1152x^32+208x^33+144x^34+24x^35+4x^36+2x^39

The gray image is a linear code over GF(3) with n=126, k=11 and d=63.
This code was found by Heurico 1.16 in 8.87 seconds.