The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 0 1 1 0 1 1 2X 1 1 1 0 1 1 1 2X 1 1 X 2X 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 X+2 1 1 0 2X+1 2 2X+1 0 1 2 X 1 2X+1 X+2 1 2 1 0 1 2X+1 2X 2 1 X 2X+1 1 1 0 2X+2 X 1 2X X+1 X+2 2X+1 2X X+2 0 X 2X 1 X
0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 X 2X X 2X X 2X 0 X X 2X X 2X 0 2X 2X 2X X 2X X 0 0 2X X 2X 2X 0 2X 2X 0 0 2X 2X X 0 X 0 2X X 2X 2X 0
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 X 2X 0 X X 2X 0 X X X 2X 0 X X X X 2X X 2X 0 2X X 2X 0 X 2X 2X 0 0 2X 2X 0 0 2X 0 X 2X X
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X 2X 0 0 2X X X 2X 0 X 2X 0 2X X X X 2X 0 0 X 0 2X 0 X 0 0 2X 0 2X 0 0 2X 2X 2X 0 2X X 0 2X 2X 2X X 0
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 2X 2X 0 2X 2X X 2X 0 X 2X X 0 2X 0 0 X 0 X 2X 0 X 0 0 0 0 2X 0 0 0 2X 2X 2X 0 0 2X 2X X 2X X X 2X
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 2X 0 2X 0 2X 2X 2X 2X 2X 2X 0 0 0 2X 0 2X X X X 2X 2X X 0 2X 2X 0 2X X 0 0 0 X 0 X X 0 2X X X X X
generates a code of length 56 over Z3[X]/(X^2) who´s minimum homogenous weight is 96.
Homogenous weight enumerator: w(x)=1x^0+126x^96+48x^97+246x^99+330x^100+468x^102+798x^103+652x^105+1440x^106+824x^108+2244x^109+1082x^111+2928x^112+1252x^114+2646x^115+832x^117+1830x^118+560x^120+696x^121+180x^123+132x^124+142x^126+24x^127+92x^129+6x^130+56x^132+34x^135+12x^138+2x^141
The gray image is a linear code over GF(3) with n=168, k=9 and d=96.
This code was found by Heurico 1.16 in 25.5 seconds.