The generator matrix
1 0 0 0 0 0 0 0 1 1 1 X 1 1 1 1 X X 1 1 X X X X 1 1 1 1 X 1 1 X X 0 1 0 1 X 0 1 X 1 0 X 0 0 1 X X 0 X 0 1 1 0 X 1 0 0 1 X 1 X 1 X 0 1 X 1 X 0 1 0 X 1 0 1 1 1 0 0 1 1 X 1 1 1 1
0 1 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 0 X 0 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X+1 X+1 1 1 X+1 1 0 1 1 X+1 1 0 1 1 X+1 X 0 1 X X+1 0 1 X 1 X X 1 0 1 1 X 0 1 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 X X X X 1 X+1 1 1 1 1 X+1 X+1 0 1 1 0 X+1 0 X 0 X+1 1 1 X 1 1 0 X X X+1 0 X+1 1 X 0 X+1 X X 0 X+1 1 0 1 1 0 X+1 X+1 X+1 0 0 X+1 X X+1 X X+1 X 1 X 0 X X+1 X X 0 X+1 1 1 X+1 0 X 1 X 0 0
0 0 0 1 0 0 0 0 0 1 X 1 0 X+1 1 1 1 1 X+1 X X 1 1 X+1 X+1 X 0 0 0 1 0 X 0 X 0 X+1 1 1 1 0 1 0 1 X+1 X+1 0 1 X X+1 1 X+1 1 1 X X X+1 0 0 X X+1 X X+1 0 1 1 0 1 0 X 0 X 0 1 X 1 0 0 X 0 0 0 1 X+1 1 0 X+1 0 0
0 0 0 0 1 0 0 0 1 0 1 1 X 0 1 X+1 0 1 0 1 X+1 X 1 1 1 0 0 1 1 X X 1 0 1 1 X+1 X+1 X+1 X 1 X 0 0 0 1 1 0 X 1 X 0 X+1 0 0 X X X+1 1 X X+1 1 X X+1 X 1 1 0 1 X 1 0 X 0 X X+1 X+1 0 X X+1 0 1 1 X 1 X X X 0
0 0 0 0 0 1 0 0 1 X 0 X+1 1 X+1 0 1 1 X 0 1 1 0 1 0 X+1 X X X+1 X 0 1 1 1 X X 1 0 X X+1 0 X 1 X 1 X+1 X+1 X+1 X 1 0 X+1 X X+1 0 X+1 X+1 X+1 X+1 X 0 X+1 0 X+1 X X 1 X+1 1 X+1 X X X 1 0 X X 0 0 0 X 0 X X X 1 1 0 0
0 0 0 0 0 0 1 0 1 X+1 X+1 1 X+1 X 0 0 1 X+1 0 X X+1 1 0 1 1 1 0 X X 1 0 X X+1 1 1 X X X 0 1 X+1 1 X 0 X 0 1 1 0 X+1 X X X X 0 X+1 0 X+1 1 X X X+1 0 0 0 X+1 0 X 0 0 X+1 1 X+1 0 0 X+1 X 1 0 1 0 X 1 X+1 0 0 X 0
0 0 0 0 0 0 0 1 X X 1 1 1 X+1 X+1 0 X 0 X X+1 1 X+1 0 X X 1 1 X 0 1 X+1 1 X+1 1 0 1 X+1 1 X 1 1 1 0 X+1 X 1 0 1 1 0 0 X+1 1 X+1 1 X 0 0 X+1 0 X X 1 1 X+1 1 X 0 0 X+1 1 X X+1 1 0 X+1 1 0 X+1 X X X+1 X X 1 X X 0
generates a code of length 88 over Z2[X]/(X^2) who´s minimum homogenous weight is 70.
Homogenous weight enumerator: w(x)=1x^0+64x^70+489x^72+1044x^74+1828x^76+2894x^78+3892x^80+5236x^82+6154x^84+6994x^86+7783x^88+7378x^90+6603x^92+5326x^94+4026x^96+2644x^98+1577x^100+830x^102+461x^104+190x^106+69x^108+36x^110+11x^112+4x^114+1x^116+1x^120
The gray image is a linear code over GF(2) with n=176, k=16 and d=70.
This code was found by Heurico 1.11 in 310 seconds.