The generator matrix

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

generates a code of length 60 over Z3[X]/(X^3) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+618x^112+990x^113+2596x^114+2724x^115+3282x^116+5466x^117+5334x^118+4896x^119+7086x^120+5910x^121+4602x^122+5380x^123+3690x^124+2184x^125+2382x^126+1062x^127+504x^128+150x^129+78x^130+42x^131+16x^132+12x^133+24x^134+8x^135+12x^136

The gray image is a linear code over GF(3) with n=540, k=10 and d=336.
This code was found by Heurico 1.16 in 8.38 seconds.