The generator matrix

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

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+88x^111+78x^112+420x^113+274x^114+162x^115+444x^116+356x^117+1050x^118+798x^119+1320x^120+3606x^121+2556x^122+2328x^123+3498x^124+900x^125+288x^126+162x^127+336x^128+244x^129+114x^130+204x^131+124x^132+48x^133+114x^134+42x^135+12x^136+54x^137+22x^138+18x^139+6x^140+8x^141+6x^144+2x^168

The gray image is a linear code over GF(3) with n=549, k=9 and d=333.
This code was found by Heurico 1.16 in 1.91 seconds.