The generator matrix
1 0 0 1 1 1 0 1 1 1 1 0 X 1 0 1 0 1 X 1 X 1 1 1 X 1 X X X 0 0 1 1 1 0 1 0 1 1 1 X 1 X 0 0 1 1 1 1 1 1 1 1 X 1 1 1 X 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 X 0 1 1 1
0 1 0 1 0 1 1 0 0 1 X+1 1 1 X 0 X 0 X+1 1 X+1 1 1 0 X+1 0 X 1 1 1 1 0 X+1 X+1 X 1 1 0 0 X X X 0 1 1 1 0 1 X X 0 1 X X 1 X X+1 1 1 X 1 X+1 1 1 1 1 0 1 0 X X 1 X+1 X X+1 1 X 0 0 X 0
0 0 1 1 1 0 1 0 1 X+1 X X 1 0 1 1 1 X+1 X X 1 X+1 X X 1 X+1 X+1 1 X X 1 X+1 X+1 0 X+1 X 1 X+1 1 X 1 0 X+1 1 1 X+1 0 1 0 0 0 0 X X+1 0 1 1 X+1 X+1 1 0 0 0 X X 1 X+1 1 0 X+1 X+1 0 1 0 1 1 1 1 1 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X X X 0 X X 0 X 0 0 X X X X X 0 X 0 X X X X X X 0 0 X X X 0 0 0 X 0 0 0 X 0 0 X X X 0 0 0 X 0 X X X X 0 X
0 0 0 0 X 0 0 0 0 0 0 X X X X 0 0 X 0 0 X 0 0 X X X 0 X 0 0 0 0 X X X X X X 0 0 0 0 X X X 0 X 0 X X 0 0 X X 0 X 0 0 0 X X 0 X 0 0 0 0 X 0 0 0 X 0 0 X X 0 X 0 X
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X X 0 X X 0 X X X X 0 0 X X 0 0 X 0 X 0 X X 0 0 X 0 X X 0 X X X 0 X 0 0 0 0 0 0 X X X X X 0 0 0 0 0 X 0 X 0 0 X X 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X X 0 X 0 0 X X X 0 X 0 0 X 0 X X X X 0 0 X X X 0 X 0 0 X 0 0 0 X X X X X 0 X X 0 X X 0 X 0 0 X 0 X X 0 0 X 0 0 0 0 0 0 0
0 0 0 0 0 0 0 X 0 X X 0 0 0 X X X X 0 X 0 0 X 0 X 0 0 X 0 X 0 0 X X X X 0 0 X 0 0 0 0 X X X X 0 X 0 X 0 0 X 0 0 X X X 0 X X X 0 0 X 0 X 0 0 X 0 0 X 0 X 0 X 0 0
0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 0 0 X X 0 0 X 0 0 X X 0 X 0 0 X X 0 X 0 0 X X X 0 0 0 0 X X X X 0 0 X 0 0 0 X X 0 0 0 X 0 X X X 0 0 0 X X 0 X X X 0 X 0 0
generates a code of length 80 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.
Homogenous weight enumerator: w(x)=1x^0+33x^68+30x^69+95x^70+148x^71+168x^72+192x^73+214x^74+224x^75+227x^76+244x^77+216x^78+200x^79+222x^80+242x^81+236x^82+230x^83+179x^84+206x^85+157x^86+140x^87+118x^88+76x^89+71x^90+68x^91+49x^92+32x^93+26x^94+8x^95+17x^96+2x^97+6x^98+6x^99+8x^100+2x^102+2x^104+1x^106
The gray image is a linear code over GF(2) with n=160, k=12 and d=68.
This code was found by Heurico 1.16 in 3.42 seconds.