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

generates a code of length 85 over Z2[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+146x^64+369x^68+103x^70+477x^72+4x^73+229x^74+16x^75+567x^76+136x^77+401x^78+464x^79+655x^80+956x^81+516x^82+1568x^83+639x^84+1904x^85+595x^86+1568x^87+551x^88+956x^89+651x^90+464x^91+379x^92+136x^93+623x^94+16x^95+202x^96+4x^97+535x^98+92x^100+290x^102+16x^104+108x^106+2x^108+36x^110+8x^114+1x^146

The gray image is a linear code over GF(2) with n=170, k=14 and d=64.
This code was found by Heurico 1.16 in 81.9 seconds.