The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 X X X 1 0 X 0 1 0 1 1 1 X 0 0 1 1 0 X 1 1 1 X 1 1 1 X 1 0 1 X 1 1 1 1 X 0 0 1 X 0 X 1 0 0 X X 0 X 0 1 1 X 1 X 0 1 0 1 0 0 0 1 1 1 0 X X+1 X+1 1 1 X 0 0 0 1 X 1 X+1 1 1 0 0 1 0 X 1 X 0 X X+1 1 X+1 X X+1 X 1 0 X 1 X X+1 X 1 X X 1 0 1 1 X X X 1 1 0 1 1 X 0 X 1 0 1 1 X 0 0 1 0 1 1 0 1 0 1 1 X 0 1 1 X 1 X X 1 1 X+1 0 1 1 1 0 0 0 X+1 1 0 X+1 0 X 0 X+1 X 1 X+1 1 1 X 1 X+1 X+1 X+1 X 1 X+1 X 1 1 1 X 0 X 1 1 0 X X 1 X+1 0 0 X+1 0 X 0 0 0 1 1 0 1 1 1 0 X+1 X 1 X 1 X+1 0 1 0 X+1 0 0 1 X+1 0 X 1 X X 1 1 1 X X 1 X X 1 X+1 X+1 X+1 1 0 1 X 0 1 1 0 X X 0 0 X+1 0 1 0 1 X X X 1 0 X+1 0 X+1 X 1 X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 0 X 0 X X 0 0 X 0 0 0 X X 0 X X X 0 X X X 0 X X 0 0 0 0 X X X X X X 0 X X 0 0 X 0 X 0 0 0 0 0 X 0 0 0 0 0 0 X 0 X X X X X X X 0 0 0 X 0 0 X X 0 X 0 X 0 X X X X X X X X 0 X X X 0 0 0 X 0 0 0 X 0 X 0 0 X 0 X X 0 0 X 0 X 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 X X X 0 X X 0 0 X 0 X X 0 0 X 0 0 0 0 X X X X X X 0 0 X 0 0 X X 0 0 0 X X X 0 X X 0 X X 0 0 0 X X 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 X X 0 0 X X X X 0 0 X X 0 X X 0 X X X 0 X 0 0 0 X X 0 0 X 0 X X 0 X 0 0 0 X 0 0 0 0 0 0 X 0 0 0 X 0 X X X 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 0 0 0 X 0 0 X 0 0 X 0 X 0 X X X 0 0 0 0 0 0 X 0 0 X 0 X X 0 0 0 0 X 0 0 0 0 X 0 X X 0 X X 0 X X X 0 X X generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 57. Homogenous weight enumerator: w(x)=1x^0+50x^57+126x^58+190x^59+262x^60+258x^61+336x^62+406x^63+414x^64+410x^65+444x^66+442x^67+499x^68+546x^69+491x^70+508x^71+459x^72+454x^73+389x^74+354x^75+265x^76+246x^77+206x^78+126x^79+125x^80+78x^81+46x^82+22x^83+13x^84+6x^85+7x^86+9x^88+3x^90+1x^92 The gray image is a linear code over GF(2) with n=138, k=13 and d=57. This code was found by Heurico 1.16 in 11 seconds.