The generator matrix

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

generates a code of length 60 over Z3[X]/(X^3) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+380x^114+1536x^115+1950x^116+1488x^117+2334x^118+2184x^119+1234x^120+1986x^121+1704x^122+1168x^123+1410x^124+834x^125+422x^126+666x^127+288x^128+80x^129+6x^130+4x^135+6x^137+2x^144

The gray image is a linear code over GF(3) with n=540, k=9 and d=342.
This code was found by Heurico 1.16 in 0.795 seconds.