The generator matrix

 1  0  0  0  1  1  1 2X^2  1  1  1  1  1 2X  1  1  1  X  1  0 2X^2+X  1  1  1  1  1  1  1  X  0 2X X^2+X  1  1  1  X  1  1  1  1  1  1  1  1 X^2+2X  1  1  1  1  1 X^2+2X  1  0  1  1 X^2+X 2X  1  X  1  1
 0  1  0  0 2X^2  1 X^2+1  1  X X^2+X 2X^2+2X+2 X^2+2 X^2+X+1  1 X^2+2 2X^2+2X+1 2X+2  1 X+1 2X  1 X^2+X+2 X^2 X^2+2X 2X+1 2X^2+2 2X^2+X+2 2X^2+2X 2X^2  1  1  1 X^2+X+1 2X^2+2X+2 2X^2+X  1 X+1 X+2  1  1 2X^2+X+2 2X^2+2X+2 X^2+X+2 X^2+2X 2X 2X  X  1 X^2 2X^2  1 2X^2+2X+1  1 2X X^2+2X  1  1 X^2+1 2X^2+X 2X+1  0
 0  0  1  0 2X^2+2X+1 2X+1 2X^2+X+2 2X^2+2X+1 X+1 X+2 2X^2 2X^2+X+1 2X^2+X+2 2X+2 X^2+2 X^2+2X+1 X^2+2X+2 2X^2+2 X^2+X  1 2X^2 2X 2X^2+X+1 X^2+X+2 X^2+X 2X^2+2X X+1 X^2+X  1 X^2+X+1  1 X^2+2X 2X^2+2 2X^2+2X+2  2 X^2+X+2  1  0 X^2  X X^2+2X+1 X+1 X^2+2X  1  1 2X^2 X^2+X 2X^2+2X+2 X^2+2X 2X^2+X+2  0 X^2+X+2 X^2+1 2X^2+2X+1 X^2+2X+2 2X^2+X+2 X^2+X+2 X^2+2X  1  2  X
 0  0  0  1 2X^2+2X+2 X^2 X^2+2X+2 X^2+2X+2  1 X^2+X 2X^2+1 2X^2+2X 2X^2+2X+1  0 2X^2 2X^2+2 X^2+X+2 2X^2+2X+2 X^2+2 2X+2 2X^2+2 2X^2+2X X^2+X  1 2X^2+1 2X^2+2  2 X^2+2X+1 2X^2+2X+1 X^2+2X  1 X^2+2X+1  X X^2+X+1 X^2+2X+2 X^2+1  1 X^2+1  X  2 X+1 2X^2 X^2+X X+1  0 X^2+X+2 X^2+2X X+1 X^2+2X+2 X^2+1 X^2+X+1 X^2+X+1 X^2+X X^2 X^2+2 2X^2+2X 2X^2 X^2+2 X^2+2X+2 X^2+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+990x^111+1686x^112+4626x^113+8236x^114+10812x^115+15366x^116+22966x^117+26472x^118+37488x^119+45146x^120+49638x^121+58350x^122+60338x^123+52884x^124+46890x^125+36528x^126+22596x^127+14760x^128+9154x^129+3408x^130+1758x^131+904x^132+132x^133+78x^134+130x^135+36x^136+6x^137+24x^138+6x^139+12x^140+20x^141

The gray image is a linear code over GF(3) with n=549, k=12 and d=333.
This code was found by Heurico 1.16 in 487 seconds.