The generator matrix

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

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+77x^70+154x^71+353x^72+528x^73+728x^74+982x^75+1188x^76+1358x^77+1687x^78+1976x^79+2202x^80+2578x^81+2786x^82+3140x^83+3411x^84+3594x^85+3827x^86+3828x^87+3823x^88+3798x^89+3494x^90+3396x^91+3124x^92+2664x^93+2377x^94+1980x^95+1602x^96+1368x^97+1062x^98+708x^99+499x^100+402x^101+296x^102+186x^103+145x^104+78x^105+42x^106+30x^107+34x^108+14x^109+8x^110+4x^111+1x^112+2x^113+1x^120

The gray image is a linear code over GF(2) with n=174, k=16 and d=70.
This code was found by Heurico 1.11 in 344 seconds.