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

generates a code of length 63 over Z3[X]/(X^3) who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+270x^123+1752x^126+54x^129+108x^132+2x^189

The gray image is a linear code over GF(3) with n=567, k=7 and d=369.
This code was found by Heurico 1.16 in 37.8 seconds.