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 X X 0 X X^2 1 X 0 0 0 X 1 1 0 1 1 X^2 X^2 X 1 X^2 1 1 0 X 1 X X^2 1 1 0 X 0 X 0 0 X X^2+X 0 0 X X^2+X X^2 0 X^2+X X^2 X^2+X X^2 X X X^2+X X^2 X X 0 X X^2+X X X^2+X X X X^2 X^2 X X X^2 X^2 X 0 X X^2+X X X X^2+X 0 X 0 X^2+X X X X X^2 X X X^2 0 0 X X 0 X^2+X X 0 0 X^2+X X 0 X X^2 X X^2 0 X^2+X X X^2+X 0 X^2+X 0 X 0 X 0 X^2 X^2 X^2+X 0 X X 0 0 X X^2+X X X X X^2 X^2+X X^2+X X^2 X^2+X X X^2 X^2+X 0 X^2 X^2 X X X^2+X X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 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+186x^44+290x^46+40x^47+763x^48+192x^49+1014x^50+480x^51+1772x^52+832x^53+2028x^54+1008x^55+2300x^56+832x^57+1694x^58+480x^59+1189x^60+192x^61+514x^62+40x^63+346x^64+90x^66+78x^68+14x^72+2x^74+7x^76 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 16.8 seconds.