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

generates a code of length 63 over Z3[X]/(X^3) who´s minimum homogenous weight is 117.

Homogenous weight enumerator: w(x)=1x^0+212x^117+294x^120+162x^122+366x^123+648x^125+3454x^126+648x^128+396x^129+138x^132+98x^135+84x^138+54x^141+4x^144+2x^180

The gray image is a linear code over GF(3) with n=567, k=8 and d=351.
This code was found by Heurico 1.16 in 0.351 seconds.