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

generates a code of length 51 over Z3[X]/(X^3) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+494x^96+162x^98+518x^99+486x^100+648x^101+1902x^102+972x^103+648x^104+340x^105+130x^108+150x^111+82x^114+24x^117+2x^123+2x^144

The gray image is a linear code over GF(3) with n=459, k=8 and d=288.
This code was found by Heurico 1.16 in 61.8 seconds.