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

generates a code of length 63 over Z3[X]/(X^3) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+60x^121+36x^123+204x^124+1644x^126+108x^127+66x^130+18x^132+48x^133+2x^189

The gray image is a linear code over GF(3) with n=567, k=7 and d=363.
This code was found by Heurico 1.16 in 0.133 seconds.