The generator matrix

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

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+58x^99+114x^101+212x^102+414x^104+274x^105+612x^107+304x^108+786x^110+382x^111+906x^113+306x^114+978x^116+262x^117+450x^119+176x^120+84x^122+100x^123+30x^125+38x^126+30x^129+18x^132+10x^135+10x^138+4x^141+2x^144

The gray image is a linear code over GF(3) with n=168, k=8 and d=99.
This code was found by Heurico 1.16 in 0.621 seconds.