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 X 1 0 X X^2 X 1 X 0 1 1 X X^2 X X X X^2 1 1 0 0 X^2 X 0 X 0 0 0 X X^2+X X 0 X^2 X^2 X X^2+X 0 X^2+X X X^2 X^2 X^2+X 0 X^2 X X^2 X X 0 X X X X^2 X 0 0 X^2 0 X X X^2 X^2+X 0 X X^2 X X X X^2+X X^2+X 0 X X X X 0 X 0 0 0 X 0 X X X^2+X 0 0 0 X X^2 X X^2+X X^2 X X^2 0 X^2+X X X X^2 0 X 0 X^2+X X X^2 X X^2+X 0 X X X^2+X X 0 0 X X X^2 X X X X X X X^2 0 X X^2+X X^2 X^2 X^2 X^2 X^2 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 X^2+X X X^2+X X^2 0 X^2+X X^2+X X 0 X^2 0 X^2 X^2+X X^2+X 0 X X^2+X X^2 X X 0 X^2 X X 0 X^2+X 0 X^2 X^2 0 X^2+X 0 X^2 X^2 X^2 X X^2+X X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 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 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 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 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 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 0 X^2 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+137x^44+371x^46+24x^47+651x^48+288x^49+843x^50+880x^51+987x^52+1728x^53+1121x^54+2304x^55+1146x^56+1824x^57+1030x^58+848x^59+780x^60+256x^61+570x^62+40x^63+342x^64+143x^66+47x^68+17x^70+4x^72+1x^76+1x^78 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 16.4 seconds.