The generator matrix

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

generates a code of length 57 over Z3[X]/(X^3) who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+318x^109+534x^110+754x^111+1008x^112+630x^113+618x^114+648x^115+390x^116+580x^117+510x^118+378x^119+54x^120+84x^121+12x^122+6x^124+12x^127+8x^129+6x^132+6x^133+4x^135

The gray image is a linear code over GF(3) with n=513, k=8 and d=327.
This code was found by Heurico 1.16 in 0.155 seconds.