The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X  1  1  1  0  1  1  1  1 2X  1  1 2X^2+X  1  1  1 X^2+X  1  1  0  1  1  1  1 X^2  1 X^2+2X  1  1 2X^2+X  0  1  1  1  1 2X 2X^2+2X  1 2X^2  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X+2 2X^2+1  1 X+1  0  2  1 2X^2+X 2X^2+X+2 2X 2X^2+2X+1  1 2X^2+1 2X+2  1 X^2 X^2+2X+1 X^2+2X+2  1 2X 2X^2+1  1 2X^2+2X+1  0  2 X^2+2  1 X^2+X+2  1 X^2+2X X^2+1  1  1 2X+2 X^2+2X+2 2X^2+X+2 X+2  1  1 X^2  X X^2+2X+1
 0  0 2X^2  0 2X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 2X^2 X^2 2X^2 2X^2  0 2X^2  0 X^2  0 2X^2  0 X^2  0 2X^2  0 X^2 2X^2 X^2  0 X^2 X^2  0  0 2X^2  0 X^2 X^2 2X^2 2X^2  0 2X^2 X^2 2X^2 X^2  0
 0  0  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0 2X^2 X^2 2X^2  0 X^2  0 2X^2 X^2 2X^2 X^2 X^2  0 2X^2 X^2 X^2 X^2 X^2  0 2X^2 X^2  0 X^2 2X^2  0  0  0  0 2X^2  0 2X^2 2X^2 X^2 X^2  0 X^2 2X^2 2X^2 X^2 2X^2 2X^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+186x^96+180x^97+792x^98+498x^99+432x^100+1026x^101+404x^102+540x^103+1242x^104+386x^105+306x^106+342x^107+190x^108+28x^111+2x^114+4x^117+2x^141

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 0.13 seconds.