The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1 X^3  1  1 X^3+X^2+X  1  1 X^2  1  1  X  1  1  0  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1 X^3  1  1 X^3+X^2+X  1  1 X^2  1  1  X  1  1  1  1  0 X^2+X  1  X X^3  X  X X^2  X  1 X^3+X^2  1  X  0  X  X  X  1 X^3+X^2 X^3+X  1  1 X^3  1  1 X^2  1  1  1  1 X^3+X^2+X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1 X^3 X^3+X+1  1 X^3+X^2+X X^3+X^2+1  1 X^2 X^2+X+1  1  X  1  1  0 X+1  1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1 X^3 X^3+X+1  1 X^3+X^2+X X^3+X^2+1  1 X^2 X^2+X+1  1  X  1  1  0 X+1 X^2+X X^2+1  1  1 X^3+X^2 X^3+X^2+X  X X^2  X  X  0 X^3+X^2+X+1  1 X^3+X X^2+X  X X^3 X^3+X^2 X^3+X X^3+1  X  1 X^3 X^3+X+1  1 X^2 X^2+X+1  1 X^3+X^2+X  X X^3+X^2+1  1  1  1  0 X^3+X^2 X^3 X^2 X^2+X X^3+X X^3+X^2+X  X X+1 X^3+X^2+X+1 X^3+X+1 X^2+X+1  0 X^3+X^2

generates a code of length 98 over Z2[X]/(X^4) who´s minimum homogenous weight is 97.

Homogenous weight enumerator: w(x)=1x^0+16x^97+210x^98+16x^99+2x^100+4x^102+3x^104+2x^106+1x^116+1x^124

The gray image is a linear code over GF(2) with n=784, k=8 and d=388.
This code was found by Heurico 1.16 in 0.422 seconds.