The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1  1  1  X  1  1  X  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  X 2X 2X  X 2X 2X 2X  0  X  X  X 2X  X  0 2X 2X  X 2X  X 2X 2X  X  0  0 2X 2X  X 2X  0 2X  X 2X 2X  0  0 2X  X  X 2X  0  X 2X
 0  0  X  0  0  0  0  0  0  0  0  X 2X 2X 2X 2X  0  X  X 2X  X 2X  0  X  X  0  X  X  X  X  0  X  0  0  X  X 2X 2X  X  0  0 2X  X  0  X 2X 2X  0  X  X  0  X  0 2X  0  0
 0  0  0  X  0  0  0  0  X 2X 2X 2X  0  0  X  0  X 2X 2X  0  X  0 2X  X  0  0  X 2X 2X  0  0  X  X  X  0 2X 2X 2X 2X 2X  0 2X  0  X 2X 2X  0  0 2X  X  X  X  0 2X 2X  0
 0  0  0  0  X  0  0  X 2X  0 2X  0  0 2X 2X  X  X  X  0 2X 2X 2X  X 2X  X  X  X 2X  X  0  0  0 2X  0  0 2X  0 2X 2X  0  0 2X 2X 2X  0 2X  0  X 2X 2X 2X  0  X 2X  X  X
 0  0  0  0  0  X  0 2X 2X  X  0 2X 2X 2X 2X 2X 2X  0  0  0 2X  X  0  X  0 2X  X  X  0  0 2X  0 2X  0 2X 2X  X 2X 2X 2X  0  X 2X  0  X  0 2X  0  X  0  X  0  0 2X 2X 2X
 0  0  0  0  0  0  X 2X 2X 2X 2X 2X 2X  X  X  X  0 2X  X 2X 2X 2X  X  0 2X 2X  X 2X  0  0  X  X  X 2X  X 2X 2X  0  X  X  X  X 2X  0  X 2X  X  X  0 2X  0 2X  0 2X  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+132x^96+190x^99+222x^102+414x^105+944x^108+1650x^111+1656x^114+730x^117+160x^120+166x^123+130x^126+70x^129+52x^132+28x^135+4x^138+10x^141+2x^153

The gray image is a linear code over GF(3) with n=168, k=8 and d=96.
This code was found by Heurico 1.16 in 1.2 seconds.