The generator matrix

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

generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+58x^65+150x^66+274x^67+501x^68+770x^69+928x^70+1026x^71+1390x^72+1648x^73+1926x^74+2252x^75+2492x^76+2804x^77+3261x^78+3492x^79+3712x^80+3880x^81+3895x^82+3982x^83+3756x^84+3664x^85+3399x^86+3140x^87+2670x^88+2272x^89+1986x^90+1558x^91+1260x^92+992x^93+728x^94+528x^95+400x^96+250x^97+197x^98+108x^99+63x^100+42x^101+35x^102+22x^103+10x^104+4x^105+6x^106+2x^107+1x^110+1x^112

The gray image is a linear code over GF(2) with n=164, k=16 and d=65.
This code was found by Heurico 1.11 in 288 seconds.