The generator matrix

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

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+270x^116+318x^117+288x^118+912x^119+884x^120+216x^121+702x^122+874x^123+324x^124+666x^125+570x^126+144x^127+324x^128+12x^129+36x^131+6x^132+6x^137+4x^138+2x^144+2x^159

The gray image is a linear code over GF(3) with n=549, k=8 and d=348.
This code was found by Heurico 1.16 in 0.535 seconds.