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

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+348x^115+666x^116+684x^117+1002x^118+546x^119+456x^120+780x^121+456x^122+444x^123+510x^124+414x^125+96x^126+96x^127+12x^128+6x^130+12x^131+18x^132+6x^133+6x^139+2x^144

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 6.89 seconds.