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  X  X  0  X  X  0  1  X  X X^2  1  1  1  X  X X^2  1  1  X  X  X  1  1
 0  X 2X  0 2X^2+X 2X X^2 2X^2+X X^2+2X X^2 X^2+X X^2+2X X^2  0 X^2+X  X 2X X^2+2X 2X^2 2X^2 2X^2+X X^2+X 2X^2+2X 2X^2+2X 2X^2  X 2X^2+2X 2X^2+X 2X  X 2X^2+X 2X  X  0 X^2+X X^2+2X  X  0 X^2 X^2 X^2+X X^2+2X  X  0 X^2 X^2 2X^2+X X^2+X 2X^2+X X^2+X
 0  0 X^2 X^2 2X^2 2X^2 2X^2 X^2  0 X^2  0 X^2  0 2X^2 X^2 2X^2  0 2X^2  0 X^2  0 2X^2 X^2 2X^2 2X^2 X^2  0 2X^2  0 X^2 X^2 X^2  0  0  0 2X^2 2X^2 X^2 2X^2 X^2 X^2 X^2  0 2X^2  0 2X^2  0 2X^2 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+78x^97+228x^98+8x^99+132x^100+126x^101+10x^102+42x^103+72x^104+4x^105+18x^106+6x^107+2x^114+2x^120

The gray image is a linear code over GF(3) with n=450, k=6 and d=291.
This code was found by Heurico 1.16 in 0.0452 seconds.