The generator matrix

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

generates a code of length 64 over Z2[X]/(X^2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+20x^41+31x^42+42x^43+109x^44+122x^45+215x^46+176x^47+266x^48+388x^49+430x^50+496x^51+541x^52+644x^53+743x^54+900x^55+907x^56+1084x^57+1258x^58+1282x^59+1333x^60+1436x^61+1538x^62+1586x^63+1735x^64+1584x^65+1440x^66+1434x^67+1343x^68+1320x^69+1109x^70+1134x^71+1063x^72+854x^73+768x^74+632x^75+535x^76+532x^77+437x^78+382x^79+248x^80+160x^81+172x^82+110x^83+86x^84+40x^85+38x^86+14x^87+20x^88+6x^89+13x^90+4x^91+5x^92+2x^93

The gray image is a linear code over GF(2) with n=128, k=15 and d=41.
This code was found by Heurico 1.16 in 99.8 seconds.