The generator matrix

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

generates a code of length 56 over Z3[X]/(X^2) who´s minimum homogenous weight is 99.

Homogenous weight enumerator: w(x)=1x^0+184x^99+90x^100+234x^101+796x^102+396x^103+522x^104+1170x^105+660x^106+546x^107+1824x^108+714x^109+780x^110+1856x^111+714x^112+690x^113+1724x^114+732x^115+720x^116+1710x^117+582x^118+528x^119+1066x^120+306x^121+282x^122+440x^123+138x^124+66x^125+140x^126+36x^127+6x^128+6x^129+6x^130+14x^132+2x^135+2x^138

The gray image is a linear code over GF(3) with n=168, k=9 and d=99.
This code was found by Heurico 1.16 in 5.83 seconds.