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 0 1 X 0 X 1 1 1 1 X X X 1 X 1 1 1 X 0 0 0 0 X 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 X 0 0 1 X 1 X X+1 0 0 0 1 0 1 1 0 X+1 0 0 1 X 1 1 0 1 X X X 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 1 0 X 1 1 X X+1 X X 1 X 0 0 X+1 1 X 1 X X 0 1 1 0 0 X+1 X+1 1 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 1 1 X+1 X+1 X+1 1 X X 0 X+1 0 1 1 1 X 0 1 X X X 1 1 X+1 0 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 1 X+1 1 X+1 0 X 1 1 X+1 1 1 X X X 1 1 X X+1 0 X+1 X 0 0 0 0 X 0 1 X+1 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 X X X X 0 0 X X 0 0 X 0 X X X X X X 0 0 0 0 0 X 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 X X 0 X X X X 0 X 0 0 0 X 0 X 0 0 0 0 X X 0 X X 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 X 0 0 X 0 X X X X 0 X X X 0 X X 0 0 X 0 X X 0 0 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 X X X 0 0 X 0 X X X 0 0 X 0 0 X 0 X 0 X X X 0 X generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+89x^56+126x^57+283x^58+382x^59+452x^60+550x^61+581x^62+690x^63+762x^64+836x^65+881x^66+940x^67+1032x^68+1052x^69+1040x^70+1056x^71+924x^72+926x^73+814x^74+702x^75+578x^76+454x^77+393x^78+266x^79+217x^80+128x^81+85x^82+56x^83+32x^84+24x^85+18x^86+4x^87+6x^88+1x^90+2x^92+1x^104 The gray image is a linear code over GF(2) with n=138, k=14 and d=56. This code was found by Heurico 1.16 in 77.1 seconds.