The generator matrix

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

generates a code of length 61 over Z3[X]/(X^3) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+108x^111+126x^112+312x^113+738x^114+1512x^115+2034x^116+1924x^117+3210x^118+4836x^119+4636x^120+5040x^121+8136x^122+5286x^123+5892x^124+6474x^125+3158x^126+2658x^127+1344x^128+558x^129+384x^130+114x^131+178x^132+102x^133+60x^134+144x^135+18x^136+12x^137+26x^138+12x^139+6x^140+6x^141+2x^144+2x^150

The gray image is a linear code over GF(3) with n=549, k=10 and d=333.
This code was found by Heurico 1.16 in 8.83 seconds.