The generator matrix

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

generates a code of length 60 over Z3[X]/(X^3) who´s minimum homogenous weight is 119.

Homogenous weight enumerator: w(x)=1x^0+108x^119+558x^120+54x^122+4x^126+2x^135+2x^153

The gray image is a linear code over GF(3) with n=540, k=6 and d=357.
This code was found by Heurico 1.16 in 0.0439 seconds.