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.