The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  X  1  1  1  X  1  X  1  1  1  1  X  1 2X^2  1 2X^2  X
 0  X  0  0  0 2X 2X^2+X 2X^2+2X  X 2X^2+2X 2X^2 2X^2 2X^2+X 2X^2+2X 2X 2X^2+X 2X^2+X 2X^2+X 2X^2+2X X^2+X  0 X^2+X 2X 2X^2+2X 2X^2+2X X^2  0 X^2+2X X^2+2X 2X  X X^2+2X  X 2X^2 X^2+X X^2+X 2X^2+2X  X 2X^2+X 2X^2+X  X 2X^2 X^2 2X X^2+2X 2X  X 2X^2+2X  X 2X^2 2X^2+X  X  X  0 2X  X 2X  X 2X^2
 0  0  X  0 X^2 2X^2 X^2 2X^2  0  0 2X^2+X X^2+2X X^2+2X 2X^2+2X X^2+X  X 2X  X X^2+2X  X X^2+2X X^2+2X 2X^2+X 2X^2+X 2X^2+2X  X X^2+2X 2X 2X^2+X  X 2X^2 2X^2+2X X^2+2X 2X^2 X^2+2X X^2+X 2X^2+2X 2X^2+X  0 2X^2+2X 2X^2+X 2X^2+2X 2X 2X 2X^2+X 2X^2 2X^2+X  X 2X^2+X X^2+X 2X^2+2X X^2+2X 2X^2+2X 2X 2X^2 X^2+2X X^2+X 2X^2+X 2X
 0  0  0  X 2X^2+2X  0 2X X^2+X  X 2X 2X^2+2X X^2 2X^2  0 X^2 X^2+X X^2+X 2X^2 X^2+2X 2X 2X X^2+2X 2X X^2+X  X  X X^2+X X^2+X  X  0 2X^2+X X^2 X^2 2X^2 X^2+X 2X^2 2X^2+X  X X^2  X X^2+X 2X^2  X X^2+2X X^2+X 2X 2X^2+2X  0 X^2+2X 2X^2+X 2X 2X^2 2X^2+X X^2  X X^2+X  0 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+188x^108+168x^109+300x^110+502x^111+456x^112+522x^113+1306x^114+1158x^115+1188x^116+2610x^117+2844x^118+1962x^119+2902x^120+1170x^121+528x^122+494x^123+282x^124+150x^125+246x^126+138x^127+168x^128+184x^129+84x^130+30x^131+60x^132+18x^133+12x^134+10x^135+2x^153

The gray image is a linear code over GF(3) with n=531, k=9 and d=324.
This code was found by Heurico 1.16 in 1.8 seconds.