The generator matrix

 1  0  0  1  1  1  1  1  1  1 2X^2+2X  1  X  1  1 X^2+2X X^2+2X  1  X  1  1  1 X^2+X  1  1  1  1  1  1 X^2+2X  1  1  X  1 2X  1  1  1  1 2X^2+X  1  1 X^2+X  1  1  X  1  1  1  1 2X  1  1  1  0 2X^2+2X 2X^2+X  1  1 2X^2 X^2+2X  1  1
 0  1  0  0 X^2 2X^2+2X+1 2X^2+2X+1 X+2  1 2X^2+X+2  1 2X^2+2  1 X^2 X^2+2  1  1 X^2+X+1 2X  X 2X^2+2X 2X^2+1  1 X^2+2X+1 2X^2+X+2 2X^2+X+2  X 2X^2+1 2X^2+2  1 2X^2+X+2 2X^2+2X+2  1 2X X^2+2X 2X^2+1 2X+2 X^2+2 2X^2  1 X^2+2X X+1  1 2X^2+1 X^2+2X+2  1 X^2+2X+1 2X X+1 2X+2  1 X^2+2X X^2+2X 2X^2+X+1  1  1  1  2 X+2  1  X 2X+2  0
 0  0  1  1 2X^2+2 2X^2+2 2X^2+2X  1 X^2+1 2X^2+2X 2X^2+2X+1 2X^2+X+2 X^2+X+2  0 2X^2+1 2X^2+2X 2X+1 X^2+X  1 X+1  2 X+1 2X^2+2X+2 2X^2+2X+2 X^2  2 X^2+X+1 X+1 X+2 X+2 X^2 X^2+2X+1  0 2X^2+X+2  1 2X^2+X X+2 2X^2+1 2X X^2+2X+1  X 2X^2+2 2X^2 X^2+2X  2 X^2+X+2 X^2+2X X^2+X+1 X^2+X+2 2X^2+X  0 X^2+1 2X^2 X^2+2X+1 X^2+2X+2 2X^2+2X+1 2X^2+X+1 2X^2+X 2X+1  1  1 2X^2+1 X^2+X+1
 0  0  0 2X 2X^2 X^2  0 X^2  0 2X^2  0 2X^2 X^2  X 2X^2+2X 2X 2X^2+X X^2+X 2X^2+X 2X^2+X 2X^2+X X^2+2X 2X X^2+2X 2X 2X^2+2X X^2  X  X  X X^2+X  X X^2+X X^2+2X X^2+2X 2X^2+X X^2+X 2X^2+X X^2+2X 2X^2+2X 2X^2  X 2X^2+2X 2X^2+2X 2X^2+2X X^2+2X 2X^2+X  X 2X^2+X 2X^2 X^2 X^2 2X^2+X X^2 2X 2X^2+2X  0 2X^2+2X  X X^2+2X 2X^2+X 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+654x^116+1508x^117+2358x^118+4032x^119+6914x^120+6318x^121+9990x^122+13386x^123+12492x^124+17178x^125+20408x^126+17154x^127+18048x^128+17678x^129+10314x^130+8328x^131+5454x^132+2304x^133+1140x^134+844x^135+90x^136+294x^137+80x^138+54x^140+60x^141+54x^143+6x^147+6x^149

The gray image is a linear code over GF(3) with n=567, k=11 and d=348.
This code was found by Heurico 1.16 in 65.2 seconds.