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  X  1 2X^2 X^2+2X  1  1  1 2X  1  1  1  1  X 2X^2+2X  1  1 X^2+X 2X^2  1  1  1 X^2+2X  1 2X  1 2X^2+X  1  1  1  1  1  X  1  1  1  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 2X+1  1 2X^2+X+2  1  1 2X^2+2X  X X^2+X+1 2X 2X^2+X+2 X^2+2 2X^2+2X+1 2X^2+2X+2  1  1 X^2 X^2+1  1  1 2X^2+2X 2X^2+2X+1 2X X^2 2X^2+X+1  1 2X^2+2X+2  1 2X^2+2X X^2 X^2+2 2X^2+X  2  1 X^2+X+2 X^2+2 X^2+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 2X^2 X^2+X+2  0  1  X X+1 X^2+2X 2X^2+X  1 2X^2+2X X^2+2X+1 2X^2+2X+2 2X^2+2  1 2X+2 X+2 2X^2+X+1  0 X^2+2 2X^2+2  2 X^2+X+1  1 2X+1 X^2+2X 2X^2+2X+2 2X+1 X^2+2X+1 2X^2+1 2X^2+2X 2X^2+X+2 X^2 X^2+2X+2 2X^2+2 X^2+2X+2 2X^2 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 2X 2X^2+2X X^2+2X 2X^2+2X  X  0 2X^2+2X 2X^2+X X^2+2X  X  X 2X^2+X X^2+2X X^2+X  X 2X X^2+2X X^2+2X  X 2X^2+X  X X^2 2X^2+2X 2X^2+X  X  0 2X 2X^2+2X  X X^2 X^2 X^2+X 2X^2+X X^2 X^2+2X  0 2X^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+540x^112+1416x^113+2566x^114+3966x^115+4830x^116+8062x^117+11094x^118+10434x^119+15964x^120+17424x^121+15852x^122+21224x^123+19638x^124+13272x^125+12890x^126+8586x^127+4746x^128+2462x^129+1182x^130+384x^131+150x^132+150x^133+60x^134+98x^135+102x^136+30x^137+6x^138+6x^139+6x^140+6x^142

The gray image is a linear code over GF(3) with n=549, k=11 and d=336.
This code was found by Heurico 1.16 in 63.4 seconds.