The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X X 1 0 1 1 X 1 1 1 X 1 1 1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 X 0 X X X X 0 X 0 X 0 0 0 X X 0 X X 0 X X X X 0 0 X 0 X X X 0 0 X 0 X X 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 X 0 X 0 0 0 X X X 0 0 0 X 0 0 0 X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 X 0 X 0 X 0 0 X 0 0 0 X 0 0 0 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 0 0 X 0 X X 0 0 X 0 0 X X 0 X 0 X X 0 0 0 X X 0 X X X 0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X 0 0 0 0 X X X X 0 0 0 X X 0 0 0 0 0 0 X X X X 0 X 0 0 X 0 X 0 0 X X 0 X 0 X 0 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X 0 X X 0 0 0 0 0 0 X X 0 0 0 0 X 0 X X X 0 X X X X 0 0 X 0 0 X 0 X 0 0 X 0 X 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 0 0 0 X X 0 0 X X 0 0 X X 0 0 X X X X X X 0 0 0 0 X 0 0 X X 0 X 0 X X 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X X X X 0 X 0 X X X 0 0 X 0 X X 0 X 0 X X X 0 0 0 X 0 0 0 0 0 X X 0 X X 0 0 X X X X X 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 X 0 X X X 0 X X X 0 X X X 0 X X 0 X 0 X 0 X X X X 0 X 0 0 X X 0 0 0 0 0 X 0 0 X 0 0 X 0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X 0 0 X X 0 X X X X 0 0 X X X 0 X X 0 X X 0 X 0 X X X X 0 X 0 0 X X 0 X 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 X 0 0 0 X 0 0 0 0 0 X 0 X X 0 X X 0 X 0 X X X 0 X X X X 0 X X 0 X X X 0 X X 0 0 0 0 generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+175x^56+319x^60+48x^62+503x^64+352x^66+757x^68+448x^70+656x^72+160x^74+335x^76+16x^78+212x^80+90x^84+21x^88+2x^92+1x^116 The gray image is a linear code over GF(2) with n=138, k=12 and d=56. This code was found by Heurico 1.16 in 4.64 seconds.