The generator matrix

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

generates a code of length 57 over Z3[X]/(X^3) who´s minimum homogenous weight is 103.

Homogenous weight enumerator: w(x)=1x^0+552x^103+1668x^104+3904x^105+6642x^106+10860x^107+15030x^108+21102x^109+28434x^110+37526x^111+44448x^112+53910x^113+59190x^114+59568x^115+55170x^116+48246x^117+35502x^118+24408x^119+13132x^120+6624x^121+3294x^122+1514x^123+390x^124+84x^125+38x^126+114x^127+42x^128+12x^129+18x^130+6x^131+12x^132

The gray image is a linear code over GF(3) with n=513, k=12 and d=309.
This code was found by Heurico 1.16 in 447 seconds.