The generator matrix

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

generates a code of length 55 over Z3[X]/(X^2) who´s minimum homogenous weight is 98.

Homogenous weight enumerator: w(x)=1x^0+78x^98+160x^99+348x^101+286x^102+522x^104+270x^105+696x^107+376x^108+930x^110+346x^111+834x^113+320x^114+684x^116+212x^117+234x^119+92x^120+48x^122+46x^123+20x^126+28x^129+10x^132+10x^135+4x^138+2x^141+4x^144

The gray image is a linear code over GF(3) with n=165, k=8 and d=98.
This code was found by Heurico 1.16 in 0.633 seconds.