The generator matrix

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

generates a code of length 70 over Z2[X]/(X^2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+41x^58+126x^59+204x^60+246x^61+330x^62+342x^63+389x^64+406x^65+428x^66+446x^67+457x^68+508x^69+465x^70+488x^71+462x^72+434x^73+419x^74+408x^75+336x^76+340x^77+251x^78+196x^79+156x^80+96x^81+104x^82+36x^83+43x^84+18x^85+9x^86+6x^87+1x^94

The gray image is a linear code over GF(2) with n=140, k=13 and d=58.
This code was found by Heurico 1.16 in 10.6 seconds.