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 1 1 1 X X X^2 X 0 X^2 X 1 0 X^2 X X^2 1 X^2 1 X^2 X^2 1 0 X 0 0 0 0 0 0 0 X X^2+X X X X^2+X X X^2 X X^2 X^2+X X^2 X^2 X^2 X X 0 X^2+X X^2 X X X^2 0 X^2 X X X^2+X X X X^2+X 0 0 0 X^2 X X X 0 X^2 X X X^2 X 0 0 0 0 0 0 X 0 0 0 X X^2+X X 0 0 0 X X X^2+X X^2 X X X^2 X X^2+X X^2+X X^2+X X^2+X 0 X^2 X^2 X X^2 X 0 0 X^2 0 X^2+X X^2+X X^2 0 0 X X 0 0 X^2 0 X X^2 X^2 X^2 X^2+X X X X X 0 0 0 0 X 0 X X X^2+X 0 X X X^2 0 X^2 X^2+X X X^2+X 0 X^2 0 X X 0 0 X X X^2 0 X^2+X X^2+X X 0 0 X^2 X^2 X X X^2 0 X^2 X^2 0 X^2 X^2+X 0 X^2+X X X^2 X^2 0 X X^2 X X^2+X 0 0 0 0 0 X X 0 X^2+X X X^2 X^2+X X^2+X 0 X^2+X X X^2 0 X X^2 0 X 0 0 X^2 X^2+X X^2+X X^2 X^2+X X^2 X^2+X X^2 X X^2 X X^2 0 X^2 X^2 X^2+X X^2+X X X X 0 X X X X^2+X X^2+X X^2 X^2+X X^2+X 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 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 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 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 X^2 0 X^2 generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 44. Homogenous weight enumerator: w(x)=1x^0+68x^44+126x^45+194x^46+226x^47+442x^48+420x^49+786x^50+472x^51+1832x^52+528x^53+2888x^54+534x^55+2747x^56+636x^57+1799x^58+432x^59+865x^60+346x^61+402x^62+214x^63+167x^64+112x^65+69x^66+40x^67+18x^68+8x^69+4x^70+2x^71+3x^72+1x^74+1x^76+1x^82 The gray image is a linear code over GF(2) with n=220, k=14 and d=88. This code was found by Heurico 1.16 in 15.9 seconds.