The generator matrix

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

generates a code of length 59 over Z3[X]/(X^3) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+586x^108+1338x^109+2352x^110+3840x^111+5376x^112+6864x^113+10652x^114+11490x^115+14226x^116+18188x^117+18954x^118+19674x^119+20682x^120+14166x^121+11664x^122+8090x^123+4782x^124+1902x^125+1220x^126+552x^127+132x^128+84x^129+150x^130+48x^131+68x^132+54x^133+12x^135

The gray image is a linear code over GF(3) with n=531, k=11 and d=324.
This code was found by Heurico 1.16 in 62.4 seconds.