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 X X X X X 1 X X 1 1 X 0 X X X 1 X 1 X 1 0 X 1 1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X 0 0 X X X 0 X X X 0 X 0 X 0 X 0 X X 0 X X 0 0 0 0 X 0 0 X 0 X 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 X X X X X X 0 0 0 0 0 X X X X X 0 X 0 0 0 X 0 X 0 X X X 0 0 X X X X 0 0 X X X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X X X 0 X X X 0 X X X 0 X 0 0 X X X X X X X 0 0 X 0 0 X 0 0 X 0 0 X X 0 0 X X X X X 0 0 0 0 X 0 0 0 0 0 0 X 0 X X 0 X X X 0 X X X 0 0 0 0 0 X 0 0 0 X 0 0 X 0 X X 0 X 0 X X X 0 0 X 0 X 0 X 0 0 X X 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X X 0 0 X 0 0 X X 0 0 0 X X 0 0 0 X X 0 X 0 X 0 X 0 0 X 0 X X 0 X 0 X X X 0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 X X 0 0 X 0 0 X X 0 X 0 X 0 X 0 X 0 X X X 0 X 0 X X X 0 X 0 0 X X X 0 X X X X 0 X X 0 0 0 0 0 0 0 X 0 0 X 0 0 X 0 0 X 0 0 X 0 X X 0 0 X X X 0 0 X X 0 X X X 0 0 0 X X 0 0 X 0 0 X X 0 X X 0 0 0 X X 0 0 0 0 0 0 0 0 X 0 X X X X 0 0 0 0 X 0 0 0 X X X X 0 0 0 X 0 X 0 0 X X X 0 X 0 X 0 X X 0 0 0 X 0 X 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X X X X 0 0 X X X X X 0 X 0 X 0 X 0 X X 0 0 X X X X X X X 0 0 X 0 X X X X X X 0 X X 0 X X 0 0 generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 44. Homogenous weight enumerator: w(x)=1x^0+74x^44+6x^46+219x^48+80x^50+298x^52+164x^54+392x^56+184x^58+282x^60+70x^62+151x^64+8x^66+94x^68+20x^72+4x^76+1x^80 The gray image is a linear code over GF(2) with n=112, k=11 and d=44. This code was found by Heurico 1.16 in 0.777 seconds.