The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 X X 0 1 1 1 1 X 1 X 1 1 0 1 X 0 X 1 1 X X X 0 1 1 1 0 X X X 0 X 1 0 0 1 0 1 X 0 1 X 1 0 0 1 0 0 0 1 1 1 0 0 X+1 X+1 1 X 1 X X+1 0 X X 1 1 1 X+1 X 0 X 1 1 X 1 1 1 X 1 1 1 X 1 1 0 1 1 X X+1 X 1 X 1 X 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 X+1 X+1 X 0 1 1 0 X 0 X+1 X 1 1 0 X X 1 X+1 1 1 X+1 X 0 0 X+1 X+1 0 0 0 X X+1 X X+1 0 X+1 X+1 X 1 X+1 X+1 X+1 X+1 0 0 0 1 1 0 1 1 1 0 1 X 1 1 0 X 1 X+1 0 0 X X 1 1 1 1 1 1 0 0 0 0 X+1 1 X+1 X+1 X 0 0 1 1 X X+1 1 0 1 1 X+1 X 0 1 X+1 1 0 X+1 1 0 0 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 X X X X X X X X X X X X 0 X 0 X X 0 X X 0 X 0 X X X 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 X X X 0 0 0 X X X 0 0 X 0 0 X X 0 X X 0 X X 0 0 0 0 X X 0 X 0 X 0 0 0 X 0 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 0 X X X X X 0 0 X X 0 X X 0 X X 0 0 X X X X 0 X 0 X X 0 X X X 0 0 0 0 0 0 0 0 X 0 0 X X 0 0 X 0 0 X X X 0 0 X X 0 X X X X 0 0 X 0 X 0 X 0 0 0 X X 0 0 0 0 0 X X X 0 X 0 X 0 X 0 0 0 0 0 0 0 0 0 X 0 X 0 0 0 0 X 0 0 X 0 0 X X X X X X X 0 X X 0 X 0 0 X 0 0 0 0 X 0 X X X 0 0 0 X X X X 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 X X X X 0 0 X 0 0 X X X 0 X X 0 0 0 0 X 0 X X 0 X X 0 X 0 0 0 X 0 0 0 0 X X X X 0 0 0 X X 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+197x^44+488x^46+1075x^48+1266x^50+1754x^52+1996x^54+2556x^56+2236x^58+2013x^60+1272x^62+871x^64+386x^66+206x^68+36x^70+24x^72+5x^76+1x^80+1x^92 The gray image is a linear code over GF(2) with n=112, k=14 and d=44. This code was found by Heurico 1.16 in 56.5 seconds.