The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  0 2X  1 2X  1  1  1  X  1  1  1  X  1  1  1  1  X  1  X  0  1  1  1  1  X 2X  1  1 2X  1  X  1  1  1  1  1  1  X  1  0  1  1  1 2X  1
 0  1  0  0  0  1  2  1 2X+1  2 2X+2  1  1  0  1 2X+2 2X+1  X  1  1 2X+1 2X 2X X+2 X+2 2X 2X  1 X+2  1 2X  2  2 2X X+1  X  0  2 X+1  1  X  1  0  2  1  1 2X 2X+2 2X 2X+2  1  X X+1 2X+1 2X 2X
 0  0  1  1  2  2  2  1 2X  0 2X+1  2 2X+1  0 X+1 X+1 2X+2 X+2 X+2 2X+1  0 X+1  1  2 2X X+2  X  0 2X  1  1 2X+2 X+1 X+1 2X+2  1  1 X+1  X 2X+2 2X+1  1  2 2X 2X+2  2  1 2X+1  1 X+1  2 X+1 X+1 2X+2  1  X
 0  0  0 2X  0  0  0  0  0 2X 2X  X 2X 2X  X  0 2X 2X 2X  X 2X  0  0 2X  X  0  X  X  0 2X  X  0  X  0 2X  0 2X  X  X  X  X  0 2X  X  X 2X  X  0  0 2X 2X  X  X 2X  0 2X
 0  0  0  0  X  0  X 2X 2X 2X 2X  0  X  X 2X  X  0 2X 2X  0  X  X 2X  0  X 2X 2X  0 2X  0 2X  X 2X 2X  0  0 2X  X  X  X  0  X  X  X 2X  X 2X 2X  0  X 2X  0  X 2X  X  0
 0  0  0  0  0 2X  X  X  0  X  0  X  X  X 2X 2X  0  X  0  X 2X  X 2X  X 2X  X  X  X 2X  X  0 2X  X  0 2X  X  X  X  X  X  0  X 2X  0  0  0 2X  0 2X  X 2X 2X 2X  0  0  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+242x^99+120x^100+228x^101+788x^102+378x^103+384x^104+1356x^105+570x^106+588x^107+1508x^108+678x^109+870x^110+1814x^111+810x^112+768x^113+1788x^114+786x^115+756x^116+1814x^117+624x^118+516x^119+1030x^120+270x^121+198x^122+390x^123+102x^124+60x^125+126x^126+36x^127+6x^128+38x^129+24x^132+8x^135+2x^138+6x^141

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 9.5 seconds.