The generator matrix

1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 1 X X X X X X 1 1 1 1 1 1 1 1 X X 1 1 1 1 0 1 1 1 1 1 0 1 0 1 X 1 X 0 X 1 0 1 X 0 X 1 0 1 X 0 X 0 X 1 0 1 0 0 X 1 1 0 X 1 X 1 1 1 X 1 X X 1 1 X 1 1 1 1 1 1 1 X 0
0 1 0 0 0 0 0 X 1 1 1 1 1 1 1 0 X X 1 1 1 X 1 X 1 1 X X X+1 X+1 X+1 X+1 0 X 0 0 0 0 X X X X X 0 1 0 1 X 1 X 1 1 1 0 1 X 1 1 1 0 1 X 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 X 1 X X X 1 1 X 0 X+1 1 X X+1 X+1 X+1 1 X+1 X+1 1 0 X
0 0 1 0 1 X X+1 1 0 X+1 1 X 1 X X+1 1 0 1 0 1 X 1 X+1 X X X+1 X X+1 0 1 X+1 X 1 1 0 1 X X+1 1 0 1 X X+1 0 0 X+1 X+1 0 0 1 1 0 X+1 1 1 X+1 X+1 X+1 X X X X X 0 1 X X+1 1 1 X X 1 0 0 X+1 X+1 X 0 0 X X+1 1 1 0 0 1 0 1 1 1 X X+1 1 1 X+1 X+1 0 1
0 0 0 1 X 1 X+1 1 X+1 0 1 X X 1 X+1 X+1 1 0 1 0 X X X+1 1 X+1 X X X+1 X X+1 1 0 1 X+1 1 0 X+1 X X+1 X+1 X 1 0 X X 1 1 X X X+1 X+1 X+1 X X+1 X+1 1 1 0 X+1 0 0 0 0 1 X X+1 0 1 1 X X 0 X+1 X+1 0 X 1 0 0 X+1 X 1 1 1 1 X+1 0 0 0 1 X X+1 X 0 X 0 X X+1

generates a code of length 98 over Z2[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+122x^96+48x^98+52x^100+16x^102+10x^104+4x^108+2x^120+1x^128

The gray image is a linear code over GF(2) with n=196, k=8 and d=96.
As d=96 is an upper bound for linear (196,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8.
This code was found by Heurico 1.10 in 0 seconds.