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.