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

generates a code of length 56 over Z3[X]/(X^2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+126x^87+348x^90+596x^93+900x^96+1116x^99+1476x^102+3192x^105+8420x^108+14942x^111+15036x^114+7290x^117+1830x^120+1462x^123+1024x^126+684x^129+312x^132+168x^135+70x^138+30x^141+18x^144+4x^147+2x^150+2x^153

The gray image is a linear code over GF(3) with n=168, k=10 and d=87.
This code was found by Heurico 1.16 in 78.3 seconds.