The generator matrix

 1  0  1  1  1  X  1  1  0  1  1  X  1  1  0  1  1  X  1  1  1  1  0  X  1  1  1  1  0  X  1  1  1  1  0  X  1  1  X  X  0  1  1  0  X  X  X  0  1  1  1  1  0  X  X  X  0  1  1  1  1  X  X  0  1
 0  1 X+1  X  1  1  0 X+1  1  X  1  1  0 X+1  1  X  1  1  0  X X+1  1  1  1  0  X X+1  1  1  1  0  X X+1  1  1  1  0  X  0  X  X X+1  1  1  1  0  X  X  0  X X+1  1  1  1  0  X  X  0  X X+1  1  0  X  X  0

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+3x^68+8x^69+3x^70+1x^74

The gray image is a linear code over GF(2) with n=130, k=4 and d=68.
As d=68 is an upper bound for linear (130,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.0431 seconds.