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

generates a code of length 96 over Z2[X]/(X^2) who´s minimum homogenous weight is 101.

Homogenous weight enumerator: w(x)=1x^0+8x^101+3x^102+3x^104+1x^110

The gray image is a linear code over GF(2) with n=192, k=4 and d=101.
This code was found by Heurico 1.16 in 0.178 seconds.