The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  0  X  1  1  1  1  0  1  X  1  0  1  0  X  1  0  1  0  1  0  X  X  1  1  1  1  X  1  1  0  X  0  X  1  1  0  1  0  0  0  X  1  X  0  1  1  1  1  X  0  1  1  X  X  1  1  1  1  1  0  X  1  1  0  1  1  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  1  1  1  X X+1  1  X  X  1  X  X  0  1  1 X+1  0 X+1  1  X  1  0  1  0  X  0 X+1  0 X+1  0  X  0  1  X  1  X  1 X+1  X  X  1  X X+1  X  X  1 X+1 X+1 X+1  1  X  0 X+1  X  X  0 X+1  1  X  1  1  1  X X+1  1  1  0 X+1  0
 0  0  1  0  0  0  1  1  1  1  X  1  0 X+1 X+1 X+1  X X+1  0  0  X  0  1  1 X+1 X+1  0  1  1  X  0 X+1  X X+1  X  1 X+1  0  1  X  0  1  X  1  1 X+1 X+1 X+1  1  1  1 X+1  X  X  1  1  1 X+1  0  X  0  X  1  X  0  0  X  0  X  X X+1 X+1  X  1  X  1  0  X  X  1
 0  0  0  1  0  1  1  0  1  0 X+1 X+1  1  X X+1 X+1  X  0  1  1  0  X  0  X  0 X+1 X+1 X+1  1  X  0  0  1 X+1 X+1 X+1  X  0 X+1  0  X  X  0  1  1  X  X  X  0  0  1  0  1  X  1  1  X  1  1  1  1  1 X+1 X+1  X  1  0  0 X+1  1 X+1  X X+1 X+1 X+1  0  X  0  0 X+1
 0  0  0  0  1  1  0  1  1  X  0  X  1 X+1 X+1  0 X+1  X  0 X+1  0  X  X  1  1 X+1 X+1  X  X X+1  1  0 X+1 X+1  X X+1  X  1  1  0 X+1  1  1 X+1  0 X+1  1 X+1 X+1  X  X  0 X+1  0  1 X+1  0  1  X  X  X  1  0  1  1  0  0  X X+1 X+1 X+1  X  1  0  X X+1  0 X+1 X+1  X
 0  0  0  0  0  X  0  0  0  X  0  X  X  0  X  X  0  0  X  0  X  0  X  0  X  0  0  X  X  X  0  X  0  0  X  0  0  0  0  0  0  0  X  0  X  0  X  X  0  0  0  X  0  0  X  0  X  X  X  0  0  X  0  X  0  X  X  X  0  X  X  X  X  X  0  X  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  0  0  X  X  X  X  0  0  0  0  X  X  0  X  X  0  X  0  X  0  X  0  X  X  X  X  0  0  0  0  X  0  X  0  X  0  0  X  0  0  X  X  X  X  X  0  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  X  X  0  X  0  X  X  X  X  0  0  0  0  0  X  0  X  0  X  0  0  0  0  0  X  0  X  0  0  X  X  0  X  X  0  X  0  X  0  0  X  X  0  0  0  X  X  0  0  X  0  X  0  X  0  X  0  X  X  X  X  0  0  X  X  X  X  0  X
 0  0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  0  X  0  0  X  0  X  X  0  0  X  0  X  X  X  X  X  X  0  X  X  X  0  X  X  X  X  X  X  0  0  X  X  X  X  X  X  X  X  0  0  X  0  X  0  0  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  X  X  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+72x^66+120x^67+223x^68+288x^69+399x^70+464x^71+582x^72+624x^73+684x^74+772x^75+856x^76+862x^77+846x^78+934x^79+897x^80+982x^81+895x^82+936x^83+825x^84+808x^85+715x^86+600x^87+497x^88+408x^89+351x^90+208x^91+174x^92+106x^93+117x^94+50x^95+35x^96+18x^97+13x^98+12x^99+2x^100+2x^102+3x^104+1x^106+1x^110+1x^112

The gray image is a linear code over GF(2) with n=160, k=14 and d=66.
This code was found by Heurico 1.16 in 93.9 seconds.