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

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+15x^84+36x^85+33x^86+24x^87+26x^88+32x^89+15x^90+8x^91+18x^92+16x^93+8x^94+1x^96+8x^97+4x^98+3x^100+4x^101+3x^102+1x^154

The gray image is a linear code over GF(2) with n=178, k=8 and d=84.
This code was found by Heurico 1.16 in 0.151 seconds.