The generator matrix

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

generates a code of length 58 over Z3[X]/(X^3) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+594x^110+1158x^111+1836x^112+1920x^113+1970x^114+2184x^115+1662x^116+1602x^117+1674x^118+1542x^119+1182x^120+900x^121+738x^122+472x^123+210x^124+12x^125+6x^128+6x^129+6x^131+6x^132+2x^135

The gray image is a linear code over GF(3) with n=522, k=9 and d=330.
This code was found by Heurico 1.16 in 0.74 seconds.