The generator matrix

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

generates a code of length 53 over Z3[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+102x^96+126x^97+186x^98+650x^99+258x^100+264x^101+698x^102+294x^103+282x^104+584x^105+252x^106+240x^107+546x^108+156x^109+222x^110+504x^111+198x^112+162x^113+316x^114+90x^115+78x^116+180x^117+54x^118+18x^119+56x^120+30x^121+6x^122+6x^123+2x^129

The gray image is a linear code over GF(3) with n=159, k=8 and d=96.
This code was found by Heurico 1.16 in 0.516 seconds.