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  0  0  X  1  1  1  1  1  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  1  1  1  1 X+1 X+2  X 2X  0 X+1
 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  X  1 X+2 X+2  2  X X+2 2X+1 X+1
 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  0  X 2X+1 X+2  0 X+1 2X+2  1  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+272x^102+768x^104+420x^105+852x^107+452x^108+714x^110+376x^111+618x^113+258x^114+504x^116+180x^117+294x^119+124x^120+180x^122+96x^123+48x^125+6x^126+12x^128+2x^129

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 4.91 seconds.