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  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  X  1  1
 0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  X  X  X  X  0  0  X  X  0  X  X  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  X  X  0  0  X  X  0  0  X  X  X  X  0  0  0
 0  0  X  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  X  X  X  X  0  0  0  X  X  0  X  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  X  X  0  0  X  X  0  X  X  X  X  0  0  0  0  0
 0  0  0  X  0  X  X  X  0  0  0  0  X  X  X  X  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  X  X  0  0  X  X  0  X  X  0  0  0  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  X  0  0  X  X  X  X  0  0  0  X  X  0  0  0  0
 0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  0  0  0  0  X  X  0  X  X  0  X  X  0  0  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  0  0  X  X  0  X  0  X  0  X  X  0  0  0

generates a code of length 97 over Z2[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+15x^96+32x^98+15x^100+1x^132

The gray image is a linear code over GF(2) with n=194, k=6 and d=96.
As d=96 is an upper bound for linear (194,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.187 seconds.