The generator matrix

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

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+276x^114+390x^115+192x^116+758x^117+1038x^118+144x^119+842x^120+912x^121+216x^122+644x^123+690x^124+96x^125+290x^126+42x^127+2x^129+6x^130+14x^132+4x^135+2x^141+2x^165

The gray image is a linear code over GF(3) with n=540, k=8 and d=342.
This code was found by Heurico 1.16 in 0.327 seconds.