The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 X X 0 1 1 1 1 0 1 X 1 0 1 X 0 1 0 X 1 1 1 1 0 1 1 X X 0 1 0 1 0 X 1 0 1 0 1 X 0 X 0 0 0 1 1 0 1 0 1 1 1 X 0 1 1 0 1 0 0 0 1 1 1 0 0 X+1 X+1 1 X 1 X X+1 0 1 1 0 1 X 1 0 X 1 X+1 X 0 0 1 X+1 X+1 1 1 X 1 1 1 X+1 1 0 1 0 0 1 X 1 0 1 0 0 0 1 X X 1 1 X 0 X+1 X 1 0 1 X+1 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 X+1 X+1 X 0 1 X+1 X+1 X 0 X 0 1 X+1 0 X 1 X X X+1 0 1 1 X+1 0 X+1 X X+1 0 1 X 1 X+1 1 X 0 X 0 1 1 0 X 1 X+1 X 0 1 1 0 X+1 X+1 1 X+1 1 0 0 0 0 1 1 0 1 1 1 0 1 X 1 1 0 X 1 X+1 X X+1 1 1 0 0 X+1 0 X 0 1 X+1 X X X+1 1 1 1 0 X X 1 X X+1 0 X 0 X 1 1 1 0 0 X 0 1 X+1 X 1 X 1 0 X+1 X X+1 1 X+1 X 1 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X 0 X 0 X X X 0 X 0 0 0 X 0 X 0 0 X X 0 X 0 X X X 0 0 X X 0 X 0 0 0 X X 0 X 0 X X X X X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 X X 0 X X X 0 0 0 X X X 0 X 0 0 0 0 0 X X 0 X X 0 X 0 0 0 X 0 X 0 X X X X 0 X X X 0 X 0 X 0 X X X 0 X 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 X X X X X X X X X X X X X X X X X X 0 0 0 X X X X X X 0 0 X X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 X X 0 0 X 0 0 X X 0 X 0 0 0 0 X X X X 0 X 0 0 X 0 0 0 0 0 X X X X X 0 0 X 0 X X X 0 0 X X X X 0 X 0 X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 X 0 0 0 0 X 0 0 0 0 X X X X 0 X 0 X 0 0 X X 0 0 0 X X 0 X X X X X 0 0 X X X 0 0 0 0 X 0 0 X 0 X X 0 0 X 0 X 0 X X 0 0 0 0 0 0 0 0 0 0 X 0 X X X X 0 0 X 0 0 X 0 X 0 X X 0 X X 0 0 X 0 0 X 0 X X 0 X X X 0 0 X 0 X X X X 0 X X X X 0 X X 0 X X X 0 X 0 X 0 0 generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 54. Homogenous weight enumerator: w(x)=1x^0+62x^54+56x^55+213x^56+226x^57+344x^58+416x^59+509x^60+622x^61+693x^62+734x^63+817x^64+916x^65+954x^66+1112x^67+1002x^68+1050x^69+977x^70+1028x^71+874x^72+842x^73+665x^74+544x^75+463x^76+354x^77+319x^78+182x^79+186x^80+80x^81+66x^82+24x^83+25x^84+6x^85+13x^86+5x^88+2x^90+1x^100+1x^106 The gray image is a linear code over GF(2) with n=136, k=14 and d=54. This code was found by Heurico 1.16 in 38.6 seconds.