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.