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  X  0  X  0  X  0  X  0  1  1  0  X  1  1  0  X  1  1  X  1  1  0  1  1  1  1  X  X  1  0  X  1  0  1  1  1  X  1  1  1  1  1 X^2  0  1  X  1  X  1  1  1  1  X
 0  X  0 X^2+X  0 X^2+X  0 X^2+X  0 X^2+X  0 X^2+X X^2+X X^2  0 X^2+X  X X^2 X^2+X X^2+X  0  X  0 X^2  0  0 X^2+X X^2+X  X  X  0 X^2 X^2+X  X X^2+X  X X^2+X  X X^2+X  X X^2+X  0  X X^2+X X^2 X^2  X X^2+X X^2+X  X  X X^2+X X^2  X X^2 X^2  0 X^2+X X^2+X X^2+X X^2  X X^2+X X^2  X X^2+X  X X^2 X^2+X  0 X^2+X  X X^2  0  X X^2 X^2  0  X  0 X^2 X^2+X  0 X^2  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0
 0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0
 0  0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0  0
 0  0  0  0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2
 0  0  0  0  0  0  0  0  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+60x^70+186x^72+271x^74+12x^75+479x^76+72x^77+708x^78+220x^79+1042x^80+480x^81+1519x^82+792x^83+1847x^84+944x^85+2016x^86+792x^87+1556x^88+480x^89+947x^90+220x^91+701x^92+72x^93+438x^94+12x^95+224x^96+129x^98+69x^100+40x^102+29x^104+14x^106+8x^108+2x^110+1x^112+1x^120

The gray image is a linear code over GF(2) with n=340, k=14 and d=140.
This code was found by Heurico 1.16 in 33.2 seconds.