The generator matrix

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

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+250x^123+702x^124+456x^126+360x^127+96x^129+198x^130+80x^132+36x^133+4x^135+4x^144

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 3.98 seconds.