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.