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

generates a code of length 53 over Z3[X]/(X^3) who´s minimum homogenous weight is 99.

Homogenous weight enumerator: w(x)=1x^0+288x^99+36x^100+780x^102+216x^103+162x^104+1362x^105+1404x^106+324x^107+1176x^108+288x^109+214x^111+148x^114+108x^117+50x^120+2x^123+2x^144

The gray image is a linear code over GF(3) with n=477, k=8 and d=297.
This code was found by Heurico 1.16 in 0.233 seconds.