The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X  1  1  1  0  1  1  1 2X^2+X  1  1  1 2X  1  1  1 X^2  1  1  1 2X  1  1  1  1  1 X^2+X  1 X^2+2X  1  1  1  1  1  1 2X  0  1  1  1  1  1  1  1  1  1  1  1 X^2+X X^2  X  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X+2 2X^2+1  1 X+1  0  2  1 2X^2+X 2X^2+2X+1 2X^2+X+2  1 2X 2X^2+1 2X+2  1 X^2 X^2+2X+1 X^2+2X+2  1 X^2+X X^2+X+1 X^2+X+2  1 2X  2 X^2+2X X^2+2 2X^2+1  1 X^2+1  1 2X 2X^2+1  2 X^2+2X X^2+1 X^2+2  1  1  0 X^2 2X^2+X 2X^2+2X 2X^2+X 2X^2+2X 2X^2+2X+1 2X+1 X+1 2X^2+X+1 X^2+X  1  X  0 2X^2+X+2
 0  0 2X^2  0 2X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 2X^2 2X^2 X^2 X^2 2X^2 2X^2  0 X^2  0 2X^2  0  0 2X^2 X^2 X^2 X^2  0  0 2X^2 X^2 2X^2 X^2 X^2  0 2X^2 X^2 X^2  0 2X^2  0  0 X^2 2X^2 X^2  0 X^2  0 2X^2 X^2  0 2X^2  0 X^2 2X^2 2X^2  0 2X^2
 0  0  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0 2X^2 X^2 2X^2  0 X^2 X^2 2X^2 2X^2 X^2  0 X^2  0 2X^2 X^2 X^2 X^2 2X^2  0  0  0 X^2  0  0 X^2 X^2  0 2X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0  0  0 2X^2 2X^2  0 X^2 X^2  0 X^2 2X^2  0 2X^2  0  0 X^2 2X^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+350x^120+162x^121+576x^122+1048x^123+288x^124+432x^125+932x^126+270x^127+648x^128+954x^129+216x^130+288x^131+296x^132+36x^133+44x^135+8x^138+6x^141+4x^144+2x^165

The gray image is a linear code over GF(3) with n=567, k=8 and d=360.
This code was found by Heurico 1.16 in 0.2 seconds.