The generator matrix

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

generates a code of length 50 over Z3[X]/(X^3) who´s minimum homogenous weight is 97.

Homogenous weight enumerator: w(x)=1x^0+456x^97+408x^98+8x^99+564x^100+198x^101+10x^102+312x^103+144x^104+4x^105+72x^106+6x^107+2x^114+2x^120

The gray image is a linear code over GF(3) with n=450, k=7 and d=291.
This code was found by Heurico 1.16 in 0.103 seconds.