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 1 0 0 X X 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 X X 0 X X 0 X 0 0 0 1 X 1 0 X 1 X 1 X 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 X 1 1 0 1 0 X+1 X+1 X 1 0 X X+1 1 X X+1 X+1 1 1 X 1 1 1 1 1 0 0 1 1 X X 1 X+1 0 1 X+1 1 X+1 X 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 0 X X+1 X X+1 X+1 0 1 X+1 X 1 X+1 0 1 X+1 1 1 X+1 X X X+1 0 X+1 1 X+1 1 X X 1 0 0 1 X+1 0 0 X X 1 0 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 0 X 0 1 X+1 X 0 X 1 1 0 X 0 1 1 X X+1 1 1 0 0 1 0 1 1 X+1 1 1 X+1 X X+1 X+1 0 1 0 X+1 X+1 X 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 1 X+1 0 X+1 X+1 X 0 X+1 X+1 X+1 X+1 X+1 X+1 X+1 1 X+1 0 1 X X+1 X+1 X X X 0 0 X+1 1 1 1 0 X+1 0 0 X+1 0 X X+1 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 0 X X 0 0 X X 0 0 X 0 X 0 0 0 X 0 X 0 X X 0 0 0 X X 0 0 0 X 0 X 0 0 X X 0 X 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 0 X 0 X X 0 X X 0 0 X 0 0 0 X X X 0 0 X X 0 X X 0 X X 0 0 X 0 X X X 0 0 X 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 0 X 0 0 0 0 X 0 X 0 0 X 0 0 X X X 0 0 X X X X 0 0 X X X X X X 0 X 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 0 X X 0 0 0 0 X 0 0 X X 0 0 0 0 X 0 X X 0 X X 0 X 0 X 0 X 0 X X generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 55. Homogenous weight enumerator: w(x)=1x^0+70x^55+178x^56+218x^57+361x^58+434x^59+561x^60+622x^61+660x^62+752x^63+863x^64+942x^65+959x^66+1058x^67+1013x^68+1050x^69+1046x^70+946x^71+824x^72+806x^73+700x^74+622x^75+483x^76+370x^77+320x^78+196x^79+144x^80+82x^81+43x^82+14x^83+23x^84+6x^85+4x^86+4x^87+6x^88+1x^90+1x^94+1x^110 The gray image is a linear code over GF(2) with n=136, k=14 and d=55. This code was found by Heurico 1.16 in 77 seconds.