The generator matrix

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

generates a code of length 80 over Z2[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+2x^13+1x^14+6x^15+24x^16+40x^17+52x^18+104x^19+126x^20+182x^21+280x^22+306x^23+336x^24+372x^25+416x^26+386x^27+341x^28+322x^29+247x^30+188x^31+142x^32+100x^33+56x^34+30x^35+21x^36+6x^37+4x^38+4x^39+1x^40+2x^67+4x^68+8x^69+16x^70+46x^71+60x^72+110x^73+202x^74+290x^75+384x^76+456x^77+616x^78+724x^79+802x^80+828x^81+732x^82+704x^83+596x^84+476x^85+408x^86+300x^87+176x^88+94x^89+74x^90+44x^91+24x^92+12x^93+2x^95+2x^96+1x^118+4x^120+8x^121+23x^122+42x^123+55x^124+92x^125+130x^126+202x^127+270x^128+296x^129+335x^130+370x^131+416x^132+380x^133+336x^134+338x^135+248x^136+204x^137+146x^138+60x^139+61x^140+40x^141+21x^142+12x^143+2x^144+4x^145

The gray image is a linear code over GF(2) with n=160, k=14 and d=13.
This code was found by an older version of Heurico in 0 seconds.