The generator matrix 1 0 1 1 1 0 1 1 0 1 1 X 1 1 0 0 1 1 1 1 0 X 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 0 1 X 1 1 0 1 1 1 1 1 X 1 1 0 1 1 1 X X 0 1 0 1 1 1 X 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 X X+1 1 1 0 X+1 0 X+1 1 1 0 X+1 X 1 X+1 X+1 X X+1 0 X+1 1 0 1 1 X+1 0 X+1 1 X 1 X 1 X X 1 1 1 1 X+1 X+1 1 0 X 1 X 0 1 1 1 1 X X 1 X X X 1 X+1 X+1 1 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 0 0 0 0 0 X X X X X X X X X X X X X X X X X 0 X 0 X 0 X X X X 0 X X X 0 X 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 X 0 X 0 0 X X 0 X 0 X 0 X X 0 X 0 X X 0 0 X 0 0 0 X X X X 0 X 0 0 0 X X X 0 X 0 X X 0 0 X X 0 0 X X 0 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X 0 0 X X X 0 X X X X 0 0 X X 0 0 X 0 0 X X X 0 X 0 X 0 X 0 X X X 0 0 0 X 0 X X X X X 0 X 0 0 X X X 0 0 X X 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X 0 X 0 X 0 0 X 0 0 X X 0 X 0 X 0 0 X 0 0 X 0 0 X X X 0 0 0 X 0 X X 0 X 0 X 0 X 0 X 0 X X 0 0 0 X X 0 X X 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 X X X X X X X X 0 X X X X 0 0 X X 0 X 0 X 0 0 0 0 X X X X X X X 0 X 0 X 0 0 X 0 0 0 0 X 0 X X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 X X 0 X X X 0 0 0 X 0 0 X X X X X 0 0 0 X X 0 X X X X X 0 0 X 0 0 X X 0 0 X X 0 0 X 0 X 0 0 X 0 X X 0 X 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 X 0 0 X X X X 0 0 X X X X 0 X X X 0 X X X 0 0 X X X X X X X X X X 0 X X X 0 0 0 X X 0 X X 0 X X 0 X 0 0 0 X 0 X X 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X X X 0 0 X 0 0 X X 0 X X 0 X X 0 0 0 X 0 0 0 X 0 X 0 X 0 0 0 X X 0 0 X 0 X X 0 0 0 0 0 X X 0 0 0 X 0 X X X 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 X X X 0 X 0 X X 0 X X 0 0 X X X 0 X X 0 0 X X 0 X X X 0 X 0 0 0 X X X X X X 0 0 X X X 0 X 0 X 0 X 0 0 X X 0 X X 0 0 X generates a code of length 72 over Z2[X]/(X^2) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+67x^58+188x^60+325x^62+450x^64+629x^66+915x^68+1041x^70+1029x^72+1028x^74+883x^76+645x^78+455x^80+270x^82+113x^84+63x^86+47x^88+21x^90+13x^92+6x^94+2x^96+1x^98 The gray image is a linear code over GF(2) with n=144, k=13 and d=58. This code was found by Heurico 1.16 in 27.1 seconds.