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

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+74x^48+47x^50+222x^52+156x^54+302x^56+32x^57+236x^58+64x^59+338x^60+512x^61+300x^62+960x^63+373x^64+960x^65+344x^66+960x^67+334x^68+512x^69+388x^70+64x^71+218x^72+32x^73+308x^74+118x^76+164x^78+56x^80+88x^82+12x^84+16x^86+1x^114

The gray image is a linear code over GF(2) with n=130, k=13 and d=48.
This code was found by Heurico 1.16 in 28.7 seconds.