The generator matrix

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

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+40x^70+134x^71+278x^72+372x^73+482x^74+582x^75+745x^76+926x^77+967x^78+1176x^79+1325x^80+1374x^81+1565x^82+1664x^83+1820x^84+1838x^85+1926x^86+1948x^87+1707x^88+1846x^89+1695x^90+1540x^91+1405x^92+1162x^93+1016x^94+802x^95+693x^96+506x^97+387x^98+288x^99+186x^100+138x^101+98x^102+50x^103+25x^104+30x^105+15x^106+6x^107+4x^108+1x^110+2x^111+3x^112

The gray image is a linear code over GF(2) with n=172, k=15 and d=70.
This code was found by Heurico 1.11 in 76.6 seconds.