The generator matrix

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

generates a code of length 83 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+18x^78+20x^79+32x^80+50x^81+23x^82+28x^83+16x^84+15x^86+12x^87+9x^88+12x^89+5x^90+4x^91+3x^92+3x^94+2x^96+2x^97+1x^148

The gray image is a linear code over GF(2) with n=166, k=8 and d=78.
This code was found by Heurico 1.16 in 0.109 seconds.