The generator matrix

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

generates a code of length 55 over Z3[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+852x^96+2976x^99+5586x^102+7740x^105+9348x^108+11238x^111+10152x^114+6888x^117+3138x^120+912x^123+198x^126+18x^129+2x^135

The gray image is a linear code over GF(3) with n=165, k=10 and d=96.
This code was found by Heurico 1.16 in 57.3 seconds.