The generator matrix

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

generates a code of length 61 over Z3[X]/(X^3) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+666x^116+1184x^117+1476x^118+2688x^119+1782x^120+1452x^121+2370x^122+1590x^123+1302x^124+1776x^125+904x^126+534x^127+1026x^128+582x^129+252x^130+54x^131+30x^132+6x^133+2x^135+6x^137

The gray image is a linear code over GF(3) with n=549, k=9 and d=348.
This code was found by Heurico 1.16 in 0.805 seconds.