The generator matrix 1 0 0 0 0 0 0 1 1 1 0 1 X 1 1 0 X X 1 0 0 1 1 1 1 1 X 1 0 1 X 1 1 0 X 1 X 1 0 1 X X 0 1 X 1 1 0 0 1 0 X 1 0 1 1 0 X 1 1 X 1 0 0 X 1 X X 1 X 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 X X 1 X+1 1 1 X+1 1 X+1 X+1 1 1 X+1 X X+1 1 X+1 0 0 1 X 1 X 1 X+1 X 1 X 0 0 X+1 X 1 X 1 1 1 0 0 1 X+1 1 1 X X 1 1 1 X 0 X 1 0 X 0 0 0 1 1 X 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 X 0 X 0 X X X X 0 0 X 0 X X 0 X 0 1 1 1 X+1 1 1 1 1 1 1 1 1 X+1 1 X+1 1 1 1 1 X+1 0 X 1 X+1 X X+1 1 X+1 X 0 X+1 1 1 0 X+1 0 1 0 0 X 0 0 X+1 0 1 0 0 0 0 1 0 0 0 0 1 0 X 1 1 0 1 1 1 1 1 X 1 X 0 X+1 X 1 0 1 1 0 0 0 1 X+1 X 0 1 X+1 X+1 1 1 0 X+1 X+1 0 0 X X X X X X+1 X+1 0 0 0 1 0 X 0 X+1 X X+1 X 1 X+1 0 1 0 0 1 X+1 X+1 X X 0 0 0 0 0 0 1 0 0 0 1 1 1 X+1 X X+1 0 X+1 X X+1 0 1 0 1 X+1 X+1 X 0 X 1 1 0 X+1 0 1 1 1 X 1 0 X+1 X X+1 0 X X+1 1 X+1 X X+1 0 X 0 X X+1 X 0 X+1 X X X X 1 1 X+1 X+1 1 1 X+1 1 X+1 0 X+1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 X+1 1 0 X X 1 0 1 1 X X+1 X+1 0 X+1 1 X X X+1 X X+1 1 X 0 1 X X X 1 0 X 1 0 0 1 X+1 1 0 1 0 X+1 0 X+1 X X+1 X+1 1 1 X 0 X+1 0 0 1 0 0 1 0 0 X+1 X+1 1 X+1 1 X 1 1 0 0 0 0 0 0 0 0 1 1 X+1 X 1 X X+1 1 1 X X 1 0 0 X+1 X X+1 X+1 1 X+1 0 X X+1 X X+1 X 0 0 0 X+1 1 X+1 0 X+1 1 1 0 1 1 X 0 1 0 1 X X+1 1 X+1 X+1 0 X+1 0 X+1 0 0 0 X+1 X X X 0 X+1 X X+1 X+1 X X+1 1 1 0 0 0 0 0 0 0 0 0 X X 0 X 0 X 0 0 X X 0 X 0 X X 0 X X 0 X 0 0 X X 0 X X X X X 0 X 0 0 X 0 X 0 X X X X 0 0 0 0 0 0 X X X 0 X X 0 0 0 X X 0 0 X X X X X X X 0 0 generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 61. Homogenous weight enumerator: w(x)=1x^0+34x^61+64x^62+194x^63+305x^64+450x^65+632x^66+704x^67+811x^68+956x^69+1161x^70+1282x^71+1443x^72+1652x^73+1739x^74+1818x^75+1955x^76+2130x^77+1979x^78+1854x^79+1894x^80+1644x^81+1564x^82+1428x^83+1191x^84+1040x^85+782x^86+586x^87+461x^88+340x^89+219x^90+158x^91+107x^92+64x^93+45x^94+36x^95+24x^96+10x^97+5x^98+4x^99+1x^102+1x^114 The gray image is a linear code over GF(2) with n=154, k=15 and d=61. This code was found by Heurico 1.11 in 65.2 seconds.