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

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+786x^96+3146x^99+5406x^102+7542x^105+9942x^108+10920x^111+10362x^114+6552x^117+3192x^120+966x^123+202x^126+30x^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 75.8 seconds.