The generator matrix

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

generates a code of length 57 over Z3[X]/(X^3) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+534x^104+794x^105+1956x^106+4152x^107+5594x^108+6870x^109+11010x^110+11030x^111+14976x^112+18786x^113+18038x^114+19512x^115+21354x^116+14544x^117+11712x^118+8172x^119+4076x^120+1662x^121+1410x^122+482x^123+114x^124+126x^125+84x^126+48x^127+42x^128+32x^129+12x^130+24x^131

The gray image is a linear code over GF(3) with n=513, k=11 and d=312.
This code was found by Heurico 1.16 in 57.9 seconds.