The generator matrix

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

generates a code of length 80 over Z2[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+74x^66+98x^67+238x^68+318x^69+443x^70+456x^71+613x^72+654x^73+674x^74+730x^75+806x^76+950x^77+857x^78+916x^79+812x^80+974x^81+839x^82+858x^83+807x^84+732x^85+711x^86+676x^87+580x^88+376x^89+398x^90+254x^91+207x^92+144x^93+88x^94+40x^95+30x^96+12x^97+10x^98+4x^99+2x^100+1x^106+1x^134

The gray image is a linear code over GF(2) with n=160, k=14 and d=66.
This code was found by Heurico 1.10 in 14.8 seconds.