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

generates a code of length 64 over Z2[X]/(X^2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+58x^46+141x^48+232x^50+342x^52+446x^54+640x^56+1027x^58+1636x^60+2316x^62+2605x^64+2336x^66+1746x^68+1076x^70+657x^72+446x^74+282x^76+186x^78+109x^80+48x^82+24x^84+14x^86+6x^88+7x^90+2x^92+1x^104

The gray image is a linear code over GF(2) with n=128, k=14 and d=46.
This code was found by Heurico 1.16 in 62 seconds.