The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1  1  X  1  X  X  1  1  X
 0 X^2  0  0  0  0  0  0  0  0 X^2 2X^2 2X^2 X^2 X^2 X^2  0 2X^2 X^2 2X^2 X^2  0 2X^2  0 X^2 X^2  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2  0 2X^2  0  0 2X^2 X^2  0 2X^2  0 2X^2 X^2  0 2X^2 X^2 X^2 2X^2  0 X^2  0  0 2X^2
 0  0 X^2  0  0  0  0 X^2 2X^2 2X^2 2X^2  0  0 2X^2 X^2 2X^2 X^2  0 X^2 X^2  0 2X^2 X^2  0 2X^2 X^2 2X^2  0 X^2  0 2X^2 2X^2 2X^2 X^2  0 X^2 X^2  0 2X^2  0 X^2 2X^2 2X^2 2X^2 X^2 X^2  0  0  0  0 X^2 2X^2  0  0 2X^2
 0  0  0 X^2  0  0 X^2 2X^2  0 2X^2  0  0 2X^2 X^2 X^2 2X^2  0 X^2  0 2X^2  0 2X^2 2X^2  0 2X^2  0 X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2  0 2X^2 2X^2  0 X^2 2X^2 2X^2 X^2 2X^2  0 X^2 X^2 2X^2  0 X^2  0 X^2 X^2  0  0 2X^2 X^2
 0  0  0  0 X^2  0 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2  0 2X^2 2X^2  0 2X^2 X^2  0 2X^2 2X^2 2X^2 X^2  0  0 2X^2 X^2  0 X^2  0 X^2  0 2X^2 2X^2  0 2X^2 X^2  0 2X^2 X^2  0 2X^2  0 2X^2 X^2  0  0 2X^2 X^2  0 2X^2 2X^2 X^2 X^2
 0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2  0 2X^2  0 X^2  0  0 2X^2 X^2 2X^2  0 2X^2 X^2 X^2  0  0  0 X^2  0  0  0 2X^2 X^2 X^2 X^2 X^2 X^2  0 2X^2 2X^2  0  0 2X^2 X^2

generates a code of length 55 over Z3[X]/(X^3) who´s minimum homogenous weight is 99.

Homogenous weight enumerator: w(x)=1x^0+98x^99+24x^101+108x^102+132x^104+126x^105+312x^107+86x^108+4836x^110+68x^111+408x^113+64x^114+120x^116+50x^117+32x^120+24x^123+14x^126+22x^129+18x^132+10x^135+2x^138+2x^141+2x^144+2x^147

The gray image is a linear code over GF(3) with n=495, k=8 and d=297.
This code was found by Heurico 1.16 in 39.4 seconds.