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

generates a code of length 50 over Z3[X]/(X^3) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+286x^96+416x^99+972x^100+396x^102+52x^105+58x^108+4x^114+2x^144

The gray image is a linear code over GF(3) with n=450, k=7 and d=288.
This code was found by Heurico 1.16 in 1.35 seconds.