The generator matrix

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

generates a code of length 39 over Z3[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+104x^63+176x^66+312x^69+616x^72+1156x^75+14818x^78+1410x^81+616x^84+172x^87+152x^90+104x^93+34x^96+12x^99

The gray image is a linear code over GF(3) with n=351, k=9 and d=189.
This code was found by Heurico 1.16 in 1.74 seconds.