The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  0  1  1  1  1  X  1  1  X  1  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  0  X  X  0  X  X  0  0  X  X  0  X  X  0  0  X  X  0  X  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  X  0  0  0  X  X  X  X  X  0  X  0  X  0  X  X  0  0  0  X  0  0  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  0  X  X  0  X  X  0  0  X  X  0  X  X  0  0  X  X  0  X  X  0  X  X  0  X  0  X  0  0  X  X  0  0  X  X  0  X  X  X  X  0  X  X  0  X  0  X  X  0  X  X  0  0  X  X  0  X  0  X  0  0  0  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  0  X  X  X  0  0  0  X  X  X  X  0  0  0  X  X  X  X  0  0  0  X  X  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  X  X  0  0  X  0  X  X  X  X  0  0  0  X  X  X  0  0  0  X  0  X  0
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  0  X  X  X  X  0  0  X  0  0  X  X  0  0  X  0  0  X  0  X  X  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  0  0  X  0  0  X  X  0  X  X  X  0  X  X  X  X  X  X  0  0  X  0  0  X  X  X  X  X
 0  0  0  0  0  X  0  0  0  X  X  X  X  X  0  X  0  X  X  X  0  0  0  0  X  X  X  0  0  X  X  X  0  0  X  0  X  0  0  X  0  0  0  X  0  0  0  X  0  X  0  0  X  X  0  0  X  X  0  X  X  X  X  0  0  0  X  0  0  0  X  0  0  0  X  X  0  X  0  X  X  X  X  0  X
 0  0  0  0  0  0  X  0  X  X  X  0  0  0  0  X  0  X  X  X  0  X  X  0  0  0  X  X  0  0  X  0  0  X  X  0  0  X  0  0  X  0  X  0  X  0  0  X  X  0  X  0  0  X  0  X  X  X  X  0  X  0  0  X  X  0  X  0  0  0  0  X  X  X  0  X  0  0  X  0  X  X  0  X  0
 0  0  0  0  0  0  0  X  X  0  X  X  0  X  X  X  0  X  X  X  0  X  0  X  0  X  0  X  X  X  X  X  X  X  X  X  0  0  X  0  0  0  X  X  0  X  0  X  X  0  0  X  X  0  X  X  0  0  X  X  0  0  0  X  X  0  X  X  X  0  0  X  X  X  X  X  X  0  0  0  0  X  X  0  X

generates a code of length 85 over Z2[X]/(X^2) who�s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+52x^78+64x^80+32x^82+96x^84+142x^86+76x^88+24x^94+18x^96+6x^102+1x^160

The gray image is a linear code over GF(2) with n=170, k=9 and d=78.
This code was found by Heurico 1.16 in 1.72 seconds.