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

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+20x^66+6x^68+4x^70+1x^72

The gray image is a linear code over GF(2) with n=130, k=5 and d=66.
As d=66 is an upper bound for linear (130,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.0619 seconds.