The generator matrix

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

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+264x^110+500x^111+378x^112+1740x^113+1792x^114+1422x^115+4242x^116+4368x^117+3492x^118+7950x^119+5954x^120+4914x^121+7998x^122+5246x^123+2736x^124+3294x^125+1474x^126+180x^127+480x^128+194x^129+162x^131+90x^132+96x^134+46x^135+18x^137+10x^138+6x^144+2x^147

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 81.8 seconds.