The generator matrix

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

generates a code of length 56 over Z3[X]/(X^2) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+418x^105+424x^108+384x^111+382x^114+288x^117+174x^120+72x^123+30x^126+8x^132+4x^135+2x^141

The gray image is a linear code over GF(3) with n=168, k=7 and d=105.
This code was found by Heurico 1.16 in 16.1 seconds.