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

generates a code of length 54 over Z3[X]/(X^3) who´s minimum homogenous weight is 99.

Homogenous weight enumerator: w(x)=1x^0+322x^99+132x^102+312x^105+5048x^108+408x^111+120x^114+142x^117+62x^126+12x^135+2x^144

The gray image is a linear code over GF(3) with n=486, k=8 and d=297.
This code was found by Heurico 1.16 in 99.6 seconds.