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

generates a code of length 58 over Z3[X]/(X^3) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+132x^105+136x^108+144x^111+626x^114+4374x^116+636x^117+288x^120+96x^123+36x^126+48x^132+20x^135+16x^141+6x^144+2x^162

The gray image is a linear code over GF(3) with n=522, k=8 and d=315.
This code was found by Heurico 1.16 in 8.8 seconds.