The generator matrix

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

generates a code of length 60 over Z3[X]/(X^3) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+414x^115+972x^116+308x^117+612x^118+1128x^119+296x^120+534x^121+822x^122+242x^123+396x^124+618x^125+36x^126+126x^127+6x^128+2x^129+6x^130+6x^131+4x^132+18x^133+12x^134+2x^138

The gray image is a linear code over GF(3) with n=540, k=8 and d=345.
This code was found by Heurico 1.16 in 18.8 seconds.