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

generates a code of length 61 over Z3[X]/(X^3) who´s minimum homogenous weight is 117.

Homogenous weight enumerator: w(x)=1x^0+258x^117+702x^118+696x^119+1156x^120+582x^121+504x^122+476x^123+552x^124+468x^125+430x^126+414x^127+114x^128+158x^129+6x^130+16x^132+6x^133+6x^135+6x^138+6x^139+4x^144

The gray image is a linear code over GF(3) with n=549, k=8 and d=351.
This code was found by Heurico 1.16 in 0.178 seconds.