The generator matrix

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

generates a code of length 57 over Z3[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+74x^96+18x^97+144x^98+352x^99+294x^100+528x^101+840x^102+504x^103+1470x^104+1436x^105+1092x^106+2346x^107+2230x^108+1788x^109+3840x^110+3032x^111+2274x^112+5274x^113+3346x^114+2376x^115+5370x^116+3456x^117+2400x^118+3966x^119+2472x^120+1482x^121+2250x^122+1440x^123+666x^124+834x^125+636x^126+162x^127+198x^128+210x^129+60x^130+24x^131+72x^132+6x^133+44x^135+34x^138+4x^141+4x^144

The gray image is a linear code over GF(3) with n=171, k=10 and d=96.
This code was found by Heurico 1.16 in 40.7 seconds.