The generator matrix

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

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+7x^48+16x^49+7x^50+1x^66

The gray image is a linear code over GF(2) with n=96, k=5 and d=48.
As d=48 is an upper bound for linear (96,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.013 seconds.