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

generates a code of length 63 over Z3[X]/(X^3) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+222x^116+242x^117+18x^118+780x^119+556x^120+234x^121+1224x^122+1608x^123+1296x^124+1872x^125+3162x^126+2466x^127+1812x^128+1924x^129+360x^130+636x^131+222x^132+390x^134+164x^135+192x^137+92x^138+120x^140+42x^141+36x^143+4x^144+6x^146+2x^165

The gray image is a linear code over GF(3) with n=567, k=9 and d=348.
This code was found by Heurico 1.16 in 1.94 seconds.