The generator matrix

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

generates a code of length 83 over Z2[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+92x^66+128x^67+338x^68+490x^69+767x^70+818x^71+1159x^72+1392x^73+1681x^74+1940x^75+2267x^76+2492x^77+2766x^78+3184x^79+3429x^80+3666x^81+3734x^82+4102x^83+3842x^84+3978x^85+3553x^86+3446x^87+3091x^88+2750x^89+2246x^90+1864x^91+1671x^92+1156x^93+1016x^94+728x^95+530x^96+378x^97+342x^98+138x^99+162x^100+76x^101+56x^102+32x^103+22x^104+6x^105+1x^106+4x^107+1x^110+1x^126

The gray image is a linear code over GF(2) with n=166, k=16 and d=66.
This code was found by Heurico 1.11 in 339 seconds.