The generator matrix

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

generates a code of length 83 over Z2[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+264x^70+678x^72+1026x^74+1286x^76+1550x^78+1600x^80+1768x^82+1829x^84+1750x^86+1596x^88+1164x^90+865x^92+556x^94+281x^96+98x^98+51x^100+16x^102+4x^104+1x^124

The gray image is a linear code over GF(2) with n=166, k=14 and d=70.
This code was found by Heurico 1.10 in 15.8 seconds.