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  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  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  X  0  X  X  0  0  X  X  X  0  0  X  X  X  X  X
 0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X  0  0  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  0  X  X  0  X  X  X  X  0  X  X  X  X  0  0  0
 0  0  0  X  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  X  X  X  X  X  X  0  0  X  X  X  X  0  X  X  0  0  0  0  X  X  0  0  0  X  X  0  0
 0  0  0  0  X  0  X  X  X  0  0  0  0  X  X  X  X  0  0  0  X  X  X  X  X  X  0  0  0  0  X  X  0  0  X  X  X  X  0  0  0  0  0  0  0  0  X  X  0  X  X  0  X  0  X  0  X  X  0  X  0  X  X  X
 0  0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  X  X  X  0  0  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  0  X  0  X  X  0  X  0  X  0  0  X  X  X  X  X  0  0  0  0  0  X

generates a code of length 64 over Z2[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+126x^64+1x^128

The gray image is a linear code over GF(2) with n=128, k=7 and d=64.
As d=64 is an upper bound for linear (128,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.0611 seconds.