The generator matrix

 1  0  0  1  1  1  1  1  1  1 2X^2+2X  1  X  1  1 X^2+2X X^2+2X  1  1  0  1  1  1  1  1  1 2X^2  1 X^2+2X  1  0  1 2X  1  1  1  1 X^2+2X  1  1  1  1  1  0 X^2+2X  1 2X^2  1  1  1  1 2X^2  1  1 2X^2 2X^2+X X^2  1 2X^2+2X  1
 0  1  0  0 X^2 2X^2+2X+1 2X^2+2X+1 X+2  1 2X^2+X+2  1 2X^2+2  1 X^2 X^2+2  1  1 X+2 X+1 X^2+X X+1 2X 2X^2+2X 2X^2+X+1 X+2 2X+1  1 X^2+X  1 X^2+X  1 X^2+X+1 2X X^2+X+2 2X^2+X+2 2X^2 2X+2 X^2 X^2+2X+2 2X^2+2X+1 2X+1 X^2+2X+2 2X^2  1 2X^2+X  1  1 X^2+2X+1 2X^2+X+2 2X+1 X^2+2X+2  1 2X^2+1  1  1  1  1 2X^2+2 X^2+X 2X^2+2X
 0  0  1  1 2X^2+2 2X^2+2 2X^2+2X  1 X^2+1 2X^2+2X 2X^2+2X+1 2X^2+X+2 X^2+X+2  0 2X^2+1 2X^2+2X 2X+1 2X^2+X+2 2X+2  1 2X^2+X+1  2 2X^2+X+1 2X^2+2X+1 X^2 2X^2  1 2X^2+X+1  X 2X 2X^2+2 2X^2+X  1 X^2+1 2X^2+2 2X^2+X+2 X+2  1 2X^2 X^2+2X+2 X^2+X+2 2X^2 X^2+2X+2 X^2+X+1  1 2X+2  2 X^2+2X+2 2X+2 2X^2+X+1 X^2 X^2+2X+1 X^2+2X X+1 X^2+X+2 X^2+2X X^2+1 X+2  1 X^2+2X
 0  0  0 2X 2X^2 X^2  0 X^2  0 2X^2  0 2X^2 X^2  X 2X^2+2X 2X 2X^2+X X^2+X 2X X^2+X X^2+X 2X  X X^2+2X X^2+2X 2X 2X^2+2X  0  X 2X^2+2X  X 2X^2+X X^2+2X  X 2X^2+2X 2X^2+X X^2 2X^2+2X  X X^2+X 2X^2+X 2X^2 X^2 X^2+2X X^2+X X^2+2X X^2 2X^2 2X^2+X 2X^2+2X 2X  0 2X^2+X X^2+X 2X^2+2X  X X^2+X X^2+2X 2X^2 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+630x^110+1096x^111+2394x^112+4230x^113+5154x^114+7398x^115+10056x^116+11472x^117+16596x^118+16524x^119+16690x^120+22824x^121+18630x^122+13398x^123+12798x^124+7956x^125+4668x^126+2034x^127+1416x^128+622x^129+108x^130+180x^131+78x^132+114x^134+32x^135+42x^137+6x^138

The gray image is a linear code over GF(3) with n=540, k=11 and d=330.
This code was found by Heurico 1.16 in 61.8 seconds.