The generator matrix

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

generates a code of length 60 over Z3[X]/(X^3) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+168x^110+350x^111+708x^112+1392x^113+1554x^114+2562x^115+3540x^116+4552x^117+4398x^118+6096x^119+6660x^120+6900x^121+5784x^122+4950x^123+3606x^124+2766x^125+1238x^126+672x^127+426x^128+226x^129+60x^130+168x^131+118x^132+42x^133+66x^134+32x^135+6x^136+6x^137+2x^141

The gray image is a linear code over GF(3) with n=540, k=10 and d=330.
This code was found by Heurico 1.16 in 8.59 seconds.