The generator matrix

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

generates a code of length 80 over Z2[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+170x^70+409x^72+432x^74+486x^76+442x^78+471x^80+404x^82+404x^84+238x^86+259x^88+152x^90+118x^92+78x^94+28x^96+4x^98

The gray image is a linear code over GF(2) with n=160, k=12 and d=70.
This code was found by Heurico 1.10 in 1.05 seconds.