The generator matrix 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 0 0 X X 1 1 0 X 1 1 X 1 0 1 0 1 0 1 X 1 1 0 1 1 1 X 1 1 0 1 1 X 1 1 1 1 0 1 0 0 0 0 1 1 1 1 X X X X 1 X 1 X+1 X 1 1 1 0 1 1 1 0 0 1 1 X 0 1 X+1 0 0 1 X+1 X 1 X+1 0 0 0 X X X+1 1 0 1 0 0 X+1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 X 1 0 1 1 X+1 X+1 1 X+1 X 0 1 1 X 1 1 0 X X+1 1 0 0 X+1 X 0 0 1 1 0 0 X 1 1 X+1 X 0 X 1 X+1 X 1 1 0 0 0 0 0 0 1 0 1 0 1 0 1 X X+1 0 1 1 X X+1 X+1 1 X 1 X X 0 X+1 0 X 1 0 1 1 X 1 0 X X X 0 X+1 X X+1 1 X+1 0 1 1 X X+1 1 0 1 0 X+1 0 0 0 0 0 0 0 1 1 0 0 1 1 X+1 X 0 X+1 X+1 1 X 0 1 X X+1 1 X+1 1 X+1 X+1 0 X+1 1 X 0 0 0 1 1 X+1 X X 0 X X+1 X X+1 X+1 0 0 X 1 0 X+1 X+1 X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 X X X X X X 0 X X 0 X X 0 X 0 X X X X 0 X X X X 0 0 X 0 X X X X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X 0 X 0 X X X 0 0 0 X X X 0 0 X 0 X X 0 X 0 X X X 0 X X 0 0 0 X X 0 0 0 X 0 0 0 X 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X X 0 0 X X X 0 0 X X 0 X X X 0 X 0 X X 0 X 0 0 X 0 0 X 0 0 0 0 X X 0 0 X X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 X 0 X 0 0 X 0 X X X 0 X 0 0 0 X 0 X X X 0 X X 0 X 0 0 0 0 X 0 0 X 0 0 0 X X X 0 X X X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 X X X 0 X 0 X 0 0 0 0 X X X 0 0 X X X X X X X 0 0 0 X 0 0 0 X X 0 X 0 X 0 X 0 0 0 0 0 0 generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 40. Homogenous weight enumerator: w(x)=1x^0+48x^40+78x^41+124x^42+206x^43+354x^44+452x^45+513x^46+684x^47+921x^48+1094x^49+1279x^50+1590x^51+1747x^52+1848x^53+2036x^54+2190x^55+2204x^56+2218x^57+2182x^58+1952x^59+1776x^60+1588x^61+1379x^62+1128x^63+808x^64+706x^65+531x^66+366x^67+259x^68+176x^69+118x^70+62x^71+66x^72+32x^73+28x^74+14x^75+8x^76+2x^78 The gray image is a linear code over GF(2) with n=112, k=15 and d=40. This code was found by Heurico 1.16 in 99.6 seconds.