The generator matrix

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

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+492x^121+720x^122+472x^123+834x^124+756x^125+526x^126+570x^127+648x^128+288x^129+510x^130+468x^131+70x^132+168x^133+8x^135+6x^138+2x^141+6x^142+2x^144+6x^145+6x^148+2x^150

The gray image is a linear code over GF(3) with n=567, k=8 and d=363.
This code was found by Heurico 1.16 in 2.31 seconds.