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

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+180x^98+102x^99+216x^100+228x^101+716x^102+432x^103+138x^104+36x^105+54x^107+32x^108+42x^110+2x^111+6x^113+2x^147

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 0.0755 seconds.