The generator matrix

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

generates a code of length 55 over Z3[X]/(X^2) who´s minimum homogenous weight is 101.

Homogenous weight enumerator: w(x)=1x^0+384x^101+308x^102+792x^104+378x^105+768x^107+464x^108+768x^110+362x^111+612x^113+252x^114+522x^116+186x^117+330x^119+140x^120+144x^122+72x^123+42x^125+24x^126+12x^128

The gray image is a linear code over GF(3) with n=165, k=8 and d=101.
This code was found by Heurico 1.16 in 5.44 seconds.