The generator matrix 1 0 1 1 1 0 1 1 0 1 1 X 1 1 0 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 X 1 0 1 1 1 1 1 0 X 1 0 1 1 X 1 1 1 X 1 X 1 1 1 1 0 1 0 1 1 X 0 0 1 1 X 1 1 1 0 X 1 1 1 1 0 1 1 1 X 1 0 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 X X+1 1 0 1 X+1 1 X+1 0 1 0 X+1 X X+1 1 X+1 1 0 X 1 X+1 1 X X+1 0 0 1 1 1 X+1 1 0 X 1 X X+1 X+1 1 X+1 1 0 1 0 X+1 1 X 1 X+1 X 1 1 1 X 0 1 X 1 X+1 0 1 X+1 X+1 X+1 0 1 X+1 0 X 1 1 0 1 1 X+1 1 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 X X X 0 X 0 X 0 X X 0 0 X X 0 X X X 0 0 0 X X X X X 0 0 0 X X X X 0 0 X 0 0 0 X 0 0 0 X 0 0 X X 0 0 X X X 0 0 0 0 X X X 0 0 0 0 0 X X 0 X X 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X 0 0 X X X X 0 0 0 0 X 0 0 0 X 0 0 X 0 X X 0 X X X X 0 0 X X 0 0 0 X 0 0 X X 0 X X X X 0 0 X X X 0 0 X 0 X X 0 X X X 0 X 0 X X 0 X 0 0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X 0 X 0 0 0 X X 0 X X 0 X X X 0 X X 0 X 0 0 0 X 0 0 X X X X X X 0 X 0 0 X 0 X X X X 0 X 0 0 0 X 0 0 X X 0 X 0 0 X X X 0 0 0 X 0 0 X X 0 0 X X 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 X X 0 X X 0 0 0 0 X 0 X X X 0 0 X X 0 0 0 X X 0 0 X X 0 0 0 0 X X X X X X X 0 X X X 0 X 0 0 0 0 X X 0 X X 0 X X 0 0 0 0 0 0 X 0 0 0 0 0 0 0 X X X 0 0 0 X 0 0 0 X 0 X X X X 0 0 0 X X X X 0 X X X 0 X 0 X 0 X 0 X 0 X X 0 X 0 X X X 0 0 0 X 0 0 X 0 0 0 0 0 X X 0 X X X 0 X 0 X 0 X X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 X 0 X X X X X X 0 0 0 0 X X 0 X X 0 X 0 0 0 X 0 0 0 X 0 X X 0 0 0 X 0 0 0 X X X 0 X 0 X 0 X X X X 0 X X X X 0 X 0 0 X 0 0 X 0 X X X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 X X 0 X X 0 0 0 X 0 X 0 0 0 X X 0 0 X X X 0 0 X X 0 X X 0 0 X X X 0 0 X X 0 X 0 X 0 X 0 0 X X X X X X X 0 X X X 0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X X X 0 X 0 X X X 0 0 0 0 X 0 0 X X X 0 0 0 X X X 0 X 0 0 0 X X 0 X 0 0 X 0 X X 0 0 X 0 X X 0 X X X X X X X 0 X X 0 X X 0 X X X X X X 0 X 0 0 X 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 0 0 X X X 0 X 0 X 0 X X 0 0 X X X 0 0 X X 0 0 X 0 X X X X X X X 0 0 0 X 0 X 0 0 0 0 X X X 0 0 0 0 X 0 X X X 0 X 0 0 X 0 X 0 0 X X X X 0 X X generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+108x^72+48x^74+430x^76+282x^78+773x^80+582x^82+1002x^84+832x^86+1109x^88+764x^90+876x^92+410x^94+504x^96+142x^98+188x^100+12x^102+91x^104+30x^108+6x^112+2x^116 The gray image is a linear code over GF(2) with n=174, k=13 and d=72. This code was found by Heurico 1.16 in 18.2 seconds.