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

generates a code of length 63 over Z3[X]/(X^3) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+168x^120+232x^123+486x^124+66x^126+972x^127+122x^129+82x^132+14x^135+18x^138+6x^141+6x^147+2x^150+10x^156+2x^159

The gray image is a linear code over GF(3) with n=567, k=7 and d=360.
This code was found by Heurico 1.16 in 8.37 seconds.