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

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

Homogenous weight enumerator: w(x)=1x^0+2x^98+44x^99+3x^100+12x^101+1x^102+1x^106

The gray image is a linear code over GF(2) with n=784, k=6 and d=392.
This code was found by Heurico 1.16 in 0.875 seconds.