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 0 X 1 1 X X 0 0 X X X 1 X 1 1 0 1 X^2 1 0 X^2 X^2 1 1 1 0 1 X X X 1 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X 0 X X 0 X^2+X X^2+X X^2+X 0 0 X^2 X^2+X 0 X X^2 X^2 X^2+X 0 X^2+X X^2 X X 0 X X^2 X^2+X X^2+X X 0 0 X^2 0 0 0 X X^2+X X^2+X X 0 X^2 X^2 X 0 0 0 0 X 0 X X X^2+X 0 0 0 X X^2 X X^2+X X 0 X^2+X X^2+X X^2 0 0 0 0 X^2+X X^2+X X^2 0 X^2+X X X^2+X X X^2 X^2+X 0 X^2+X X^2+X X^2+X 0 X X^2+X X X^2+X X X^2 0 X X^2+X X^2 X^2 X^2 X X X^2+X X^2 0 0 0 0 0 X X 0 X^2+X X 0 X 0 X X^2+X X^2+X X^2 X^2 0 0 X^2 X X^2+X 0 X X X^2 0 X X 0 X^2 X^2+X X X X X^2 0 X^2+X X^2+X X^2+X X^2 X^2+X X^2+X X^2+X X^2+X X X^2+X X^2 0 0 0 0 X^2+X X X X^2 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 44. Homogenous weight enumerator: w(x)=1x^0+48x^44+72x^45+175x^46+186x^47+259x^48+380x^49+587x^50+666x^51+906x^52+1134x^53+1317x^54+1648x^55+1627x^56+1660x^57+1339x^58+1196x^59+920x^60+644x^61+497x^62+338x^63+284x^64+180x^65+149x^66+58x^67+46x^68+22x^69+23x^70+4x^71+5x^72+4x^73+5x^74+4x^78 The gray image is a linear code over GF(2) with n=224, k=14 and d=88. This code was found by Heurico 1.16 in 16.9 seconds.