The generator matrix

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

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+276x^104+508x^105+216x^106+1506x^107+2208x^108+1620x^109+3204x^110+5502x^111+4212x^112+5376x^113+8262x^114+5454x^115+5130x^116+6992x^117+2916x^118+2586x^119+1792x^120+162x^121+576x^122+152x^123+180x^125+74x^126+114x^128+10x^129+4x^132+6x^134+4x^135+4x^138+2x^141

The gray image is a linear code over GF(3) with n=513, k=10 and d=312.
This code was found by Heurico 1.16 in 8.63 seconds.