The generator matrix

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

generates a code of length 49 over Z3[X]/(X^3) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+6x^96+180x^97+432x^98+14x^99+90x^100+2x^102+4x^120

The gray image is a linear code over GF(3) with n=441, k=6 and d=288.
This code was found by Heurico 1.16 in 0.0208 seconds.