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

generates a code of length 51 over Z3[X]/(X^3) who´s minimum homogenous weight is 98.

Homogenous weight enumerator: w(x)=1x^0+198x^98+22x^99+126x^101+1656x^102+18x^105+126x^107+2x^108+36x^110+2x^153

The gray image is a linear code over GF(3) with n=459, k=7 and d=294.
This code was found by Heurico 1.16 in 37.1 seconds.