The generator matrix

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

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+76x^52+120x^53+260x^54+302x^55+477x^56+548x^57+608x^58+730x^59+827x^60+908x^61+817x^62+956x^63+999x^64+1076x^65+980x^66+1008x^67+950x^68+852x^69+825x^70+770x^71+647x^72+464x^73+386x^74+294x^75+217x^76+120x^77+89x^78+36x^79+28x^80+8x^81+2x^82+2x^84+1x^118

The gray image is a linear code over GF(2) with n=130, k=14 and d=52.
This code was found by Heurico 1.16 in 70.1 seconds.