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 X 1 1 0 X^2 0 X X X 1 X X 1 1 0 1 X 1 X^2 1 X 0 0 X 0 0 0 0 0 0 0 X X^2+X X X X^2+X X^2 0 X X^2 X^2+X X X X^2 X X X 0 X^2 0 X^2 0 X^2 X X^2 X^2+X X^2+X X^2 0 X 0 X X 0 X 0 0 X X^2+X X^2 X^2 0 0 X^2 X 0 0 X 0 0 X 0 0 0 X X^2+X X 0 0 0 X X 0 X X^2 X X^2+X X^2+X 0 X^2 0 X^2 X^2+X X^2 X^2 X X X^2 X^2 X^2 X^2+X X X 0 X^2+X X^2 X 0 X X X^2+X 0 X X^2+X 0 X X X^2 X X^2 X^2 X^2 X^2 X 0 0 0 X 0 X X X^2+X 0 X X X^2 0 X^2 X^2+X X X 0 X^2+X X^2+X X^2 X 0 0 X^2 X X^2 X^2 X^2+X 0 X X^2+X X^2+X X X^2+X X^2+X X X^2 X^2+X X X X^2+X X^2 X^2+X 0 X^2 0 X^2 X^2 X X^2+X 0 X X^2 X^2 X^2 0 0 0 0 X X 0 X^2+X X X^2 X^2+X X^2+X 0 X^2+X X^2 X^2 X 0 0 X X^2 0 X^2+X X^2 X X X^2 X X X^2+X X 0 0 X 0 X^2 X^2+X 0 0 X X X^2 X^2+X X^2+X X X^2 X^2+X X 0 X X^2+X X^2 0 X^2+X X^2+X X 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 45. Homogenous weight enumerator: w(x)=1x^0+66x^45+130x^46+182x^47+303x^48+380x^49+484x^50+684x^51+834x^52+1108x^53+1442x^54+1574x^55+1840x^56+1736x^57+1469x^58+1260x^59+823x^60+658x^61+446x^62+318x^63+238x^64+124x^65+102x^66+72x^67+45x^68+24x^69+22x^70+6x^71+10x^72+1x^74+1x^76+1x^84 The gray image is a linear code over GF(2) with n=224, k=14 and d=90. This code was found by Heurico 1.16 in 16.4 seconds.