The generator matrix

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

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+154x^96+162x^97+522x^98+986x^99+1020x^100+1680x^101+2080x^102+2250x^103+3732x^104+4422x^105+4326x^106+6060x^107+6566x^108+6840x^109+9600x^110+9266x^111+9132x^112+12048x^113+10550x^114+10356x^115+12762x^116+10278x^117+8766x^118+10236x^119+7860x^120+5808x^121+5934x^122+4470x^123+2706x^124+2202x^125+1790x^126+816x^127+732x^128+516x^129+246x^130+102x^131+76x^132+54x^133+22x^135+4x^138+6x^139+2x^141+4x^144+2x^156

The gray image is a linear code over GF(3) with n=171, k=11 and d=96.
This code was found by Heurico 1.16 in 408 seconds.