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

generates a code of length 49 over Z3[X]/(X^3) who´s minimum homogenous weight is 94.

Homogenous weight enumerator: w(x)=1x^0+282x^94+332x^96+372x^97+162x^98+520x^99+384x^100+30x^102+36x^103+4x^105+42x^106+2x^108+12x^109+6x^112+2x^135

The gray image is a linear code over GF(3) with n=441, k=7 and d=282.
This code was found by Heurico 1.16 in 0.543 seconds.