The generator matrix

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

generates a code of length 58 over Z3[X]/(X^3) who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+504x^106+1158x^107+2736x^108+3558x^109+4668x^110+7194x^111+10350x^112+11502x^113+15958x^114+17874x^115+18510x^116+20674x^117+19278x^118+14556x^119+12032x^120+7914x^121+3984x^122+2660x^123+1074x^124+414x^125+166x^126+114x^127+90x^128+46x^129+60x^130+30x^131+6x^132+24x^133+6x^134+6x^135

The gray image is a linear code over GF(3) with n=522, k=11 and d=318.
This code was found by Heurico 1.16 in 59.2 seconds.