The generator matrix

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

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+162x^106+342x^107+738x^108+1260x^109+1998x^110+2532x^111+2880x^112+4848x^113+4886x^114+5532x^115+6588x^116+6402x^117+6066x^118+5904x^119+3784x^120+1962x^121+1314x^122+638x^123+450x^124+264x^125+134x^126+90x^127+90x^128+68x^129+54x^130+30x^131+14x^132+12x^133+6x^134

The gray image is a linear code over GF(3) with n=522, k=10 and d=318.
This code was found by Heurico 1.16 in 8.25 seconds.