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

generates a code of length 61 over Z3[X]/(X^3) who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+6x^109+42x^110+194x^111+150x^112+132x^113+388x^114+330x^115+396x^116+524x^117+1470x^118+1134x^119+578x^120+3552x^121+2232x^122+750x^123+3624x^124+1506x^125+598x^126+894x^127+228x^128+378x^129+132x^130+120x^131+136x^132+42x^133+42x^134+20x^135+6x^136+18x^138+18x^141+10x^144+18x^147+4x^150+8x^153+2x^156

The gray image is a linear code over GF(3) with n=549, k=9 and d=327.
This code was found by Heurico 1.16 in 39.9 seconds.