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

generates a code of length 48 over Z2[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+62x^48+1x^96

The gray image is a linear code over GF(2) with n=96, k=6 and d=48.
As d=48 is an upper bound for linear (96,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.0206 seconds.