The generator matrix

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

generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+75x^64+124x^65+383x^66+384x^67+666x^68+886x^69+1203x^70+1280x^71+1552x^72+1932x^73+2278x^74+2672x^75+2841x^76+3182x^77+3541x^78+3730x^79+3702x^80+4006x^81+3727x^82+4010x^83+3689x^84+3420x^85+3146x^86+2790x^87+2296x^88+1954x^89+1665x^90+1156x^91+971x^92+686x^93+538x^94+302x^95+258x^96+158x^97+134x^98+50x^99+73x^100+34x^101+19x^102+10x^103+4x^104+2x^105+5x^106+1x^110

The gray image is a linear code over GF(2) with n=162, k=16 and d=64.
This code was found by Heurico 1.11 in 322 seconds.