The generator matrix 1 0 0 1 1 1 0 1 1 1 1 0 X X 1 1 1 1 X 0 X 1 1 0 0 1 1 X 1 0 0 1 0 1 1 1 X X 1 1 X 1 0 1 1 1 X 1 0 X 1 1 X X 0 1 0 1 0 1 0 1 1 0 0 1 X+1 1 X 1 0 X 1 X+1 1 1 X 0 X+1 1 0 X+1 1 1 1 1 X X+1 1 0 1 X 1 1 0 1 X 0 0 X+1 0 1 1 X 1 1 0 0 X X 0 0 0 0 1 1 1 0 1 0 1 1 0 X 1 X+1 X+1 X X+1 0 1 0 1 0 X X+1 1 X+1 X+1 X+1 X 0 1 X+1 1 X+1 0 0 1 X X X 1 X 1 X X X+1 0 X+1 X+1 1 X+1 X+1 1 1 X 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X 0 0 X 0 0 X 0 X 0 0 0 X 0 X X 0 X X 0 X X 0 0 0 X X 0 0 X X 0 0 0 0 0 0 X 0 0 0 0 0 X X X 0 X X 0 0 X 0 X X X X 0 0 X X 0 X X 0 X 0 X 0 0 0 0 X X X 0 X 0 0 0 0 0 X 0 X X 0 X 0 0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 0 X 0 X 0 0 0 X X 0 X X 0 X X X X X 0 X 0 0 X X X X X X 0 X X 0 X 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 0 X 0 X 0 0 X X X X 0 X X X X 0 0 X 0 X 0 X X X X 0 X 0 X 0 0 X 0 0 0 X 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X X X X X X 0 0 0 X X 0 0 X X 0 X 0 0 0 X X 0 X 0 0 X X 0 0 0 0 X X X 0 X 0 0 0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 0 X X X 0 0 0 X 0 X X X 0 0 X 0 X X 0 X 0 0 X 0 0 0 0 0 0 0 X X 0 X X 0 X X X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X 0 X 0 X X 0 0 0 X X 0 0 X 0 0 X X X X 0 0 0 0 0 X 0 X X 0 0 X X 0 0 0 X 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+60x^44+56x^45+165x^46+178x^47+252x^48+268x^49+367x^50+364x^51+439x^52+562x^53+488x^54+608x^55+547x^56+592x^57+525x^58+608x^59+465x^60+420x^61+354x^62+250x^63+198x^64+116x^65+113x^66+36x^67+73x^68+34x^69+32x^70+4x^71+9x^72+3x^74+3x^76+1x^78+1x^80 The gray image is a linear code over GF(2) with n=112, k=13 and d=44. This code was found by Heurico 1.16 in 8.59 seconds.