The generator matrix

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

generates a code of length 61 over Z3[X]/(X^3) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+204x^112+360x^113+948x^114+1134x^115+2208x^116+2606x^117+3258x^118+3942x^119+5088x^120+5292x^121+6504x^122+6794x^123+5682x^124+5040x^125+4366x^126+2400x^127+1440x^128+700x^129+276x^130+270x^131+98x^132+150x^133+114x^134+32x^135+48x^136+36x^137+20x^138+24x^139+12x^140+2x^141

The gray image is a linear code over GF(3) with n=549, k=10 and d=336.
This code was found by Heurico 1.16 in 8.8 seconds.