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

generates a code of length 58 over Z3[X]/(X^3) who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+144x^106+294x^107+92x^108+528x^109+648x^110+358x^111+1008x^112+1272x^113+1452x^114+2376x^115+2934x^116+2620x^117+2340x^118+1440x^119+464x^120+402x^121+318x^122+70x^123+270x^124+228x^125+30x^126+168x^127+90x^128+6x^129+30x^130+66x^131+8x^132+18x^133+6x^136+2x^153

The gray image is a linear code over GF(3) with n=522, k=9 and d=318.
This code was found by Heurico 1.16 in 1.75 seconds.