The generator matrix

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

generates a code of length 58 over Z3[X]/(X^3) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+304x^111+546x^112+804x^113+970x^114+636x^115+654x^116+568x^117+378x^118+540x^119+602x^120+372x^121+90x^122+54x^123+6x^128+6x^130+12x^131+2x^132+10x^135+6x^136

The gray image is a linear code over GF(3) with n=522, k=8 and d=333.
This code was found by Heurico 1.16 in 0.161 seconds.