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

generates a code of length 58 over Z3[X]/(X^3) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+78x^104+114x^105+138x^106+240x^107+166x^108+306x^109+408x^110+512x^111+1470x^112+438x^113+1418x^114+4458x^115+528x^116+1794x^117+4536x^118+498x^119+918x^120+462x^121+456x^122+44x^123+264x^124+204x^125+36x^126+18x^127+66x^128+12x^129+12x^130+30x^132+22x^135+16x^138+10x^141+6x^144+4x^150

The gray image is a linear code over GF(3) with n=522, k=9 and d=312.
This code was found by Heurico 1.16 in 97 seconds.