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  0 2X^2  X  X  1  X
 0  X  0 X^2 2X 2X^2+X  X 2X^2+2X 2X X^2 2X^2+X 2X^2+2X  0 2X^2+X 2X^2 2X^2  X 2X^2+2X  0 2X  X 2X^2+X 2X^2 X^2 X^2+X X^2+2X X^2+X X^2+2X 2X^2+2X X^2 X^2+2X 2X^2 X^2+2X 2X^2+X X^2+2X X^2+X X^2+X 2X^2+2X 2X^2+X  X 2X X^2+2X X^2 2X^2  0  X  0 X^2+2X  0 2X
 0  0  X 2X^2+2X X^2 2X^2+2X  X 2X^2+X X^2+2X X^2 2X^2+X 2X X^2 2X X^2+2X  0 2X^2 2X^2 X^2+X X^2+X X^2+X X^2+X 2X^2+X 2X^2+X X^2+2X 2X^2 2X^2 2X X^2+X 2X 2X^2+X 2X X^2+2X X^2+2X X^2 2X^2+2X  0 2X^2+2X  X X^2+2X  0  0 2X^2 2X^2  X 2X^2+X 2X 2X^2+X X^2+2X 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+288x^96+108x^97+162x^98+444x^99+270x^100+324x^101+342x^102+108x^103+84x^105+30x^108+18x^111+6x^114+2x^135

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 0.052 seconds.