The generator matrix 1 0 0 0 0 0 1 1 1 0 1 1 X 1 0 1 1 1 1 0 X 0 X 1 X 1 1 1 1 1 0 1 0 X 1 0 0 1 X X 1 1 1 1 X 0 X 0 0 1 1 X 1 0 0 1 0 1 0 0 1 1 0 X 1 X 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 X 1 1 1 1 1 1 X 1 X 1 X+1 1 0 0 1 X 1 1 X 0 1 1 1 1 0 X+1 X 1 1 X 0 0 X 1 X X+1 1 X+1 X X 1 1 1 1 0 1 X+1 1 1 0 1 0 X 0 0 1 0 0 0 0 0 0 0 1 1 1 X+1 1 X X+1 X+1 0 1 1 1 X X+1 0 X 1 X X+1 X X 0 0 1 X+1 X+1 1 1 1 X 1 0 X X 1 1 X 1 0 X 1 X 0 1 1 1 0 X+1 X 1 0 X+1 1 0 0 X X 0 0 0 0 1 0 0 0 1 1 1 X 1 X+1 X+1 X+1 0 X 0 X+1 X+1 1 X X+1 0 X X+1 1 0 X+1 1 X X X+1 X+1 1 X+1 X 1 1 1 0 1 0 X+1 X 1 1 1 X X+1 1 1 0 1 0 0 1 X+1 1 1 0 X X+1 1 X X 1 0 0 0 0 0 1 0 1 1 0 X+1 X 0 X X+1 1 X X+1 0 X 1 X 1 0 X+1 X+1 X+1 X 1 X+1 0 1 X X+1 0 X X 0 X+1 X X+1 X 1 X+1 X+1 0 1 1 X+1 0 X+1 X X 1 X 0 X 1 1 0 X 1 1 X 0 0 X+1 X+1 X 0 0 0 0 0 1 1 0 X+1 X+1 1 X X+1 X+1 X X+1 1 0 0 X+1 X 1 X+1 0 X+1 1 X+1 X+1 X+1 0 0 1 X X+1 X 1 X+1 X 0 1 X X X 1 0 X X+1 1 0 X+1 1 1 0 0 X+1 X+1 X+1 0 X+1 0 X+1 0 1 1 0 X 0 1 0 0 0 0 0 0 X 0 X X X 0 X X 0 X X 0 0 X 0 X X 0 X X X X X 0 0 X 0 X 0 0 0 X X 0 X X X 0 X X 0 0 X 0 0 0 X X 0 0 0 X 0 X X 0 0 X X X X 0 0 0 0 0 0 0 0 X 0 X 0 X X 0 0 0 0 X X X 0 X X 0 0 X X X X 0 X X X 0 0 X 0 0 0 0 0 0 X 0 X 0 X X X X 0 X 0 X X X X X 0 0 0 0 0 0 0 0 X 0 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+54x^55+141x^56+258x^57+361x^58+478x^59+541x^60+628x^61+700x^62+778x^63+825x^64+910x^65+992x^66+926x^67+1066x^68+1076x^69+1012x^70+884x^71+887x^72+872x^73+701x^74+636x^75+472x^76+366x^77+269x^78+180x^79+144x^80+112x^81+58x^82+32x^83+16x^84+2x^85+2x^86+2x^88+1x^94+1x^108 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 74.8 seconds.