The generator matrix

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

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+70x^78+166x^80+90x^82+57x^84+40x^86+31x^88+10x^90+20x^92+7x^94+6x^96+2x^100+6x^102+4x^104+1x^108+1x^110

The gray image is a linear code over GF(2) with n=166, k=9 and d=78.
This code was found by Heurico 1.16 in 0.153 seconds.