The generator matrix 1 0 0 0 1 1 1 0 1 1 1 X X^2+X 1 0 X^2 1 X^2 1 1 X^2+X X^2 X 1 X 0 0 X^2+X 1 1 1 1 X^2 1 X 1 0 X 1 1 1 X^2 0 0 0 1 1 X^2+X 1 X^2 1 X^2+X X^2+X X 1 1 X 1 1 X 1 0 1 1 X 1 0 1 0 0 0 1 1 1 X^2+X+1 X^2+1 X 1 X^2+X 0 1 X^2 X+1 1 X^2+X X+1 1 X^2 1 X^2 1 X^2+X 1 X X^2+X+1 X X+1 X X^2+X 0 1 X^2+1 1 0 X^2+X X^2+1 X X^2 1 1 1 0 X^2+X 1 1 1 X^2+X+1 X 1 X^2 X^2+X X^2+X+1 X X^2 0 0 X^2 1 X+1 1 1 0 0 0 1 0 1 1 0 1 X^2+1 X^2+X X X^2+1 1 X^2+X+1 0 X^2+X X^2+X+1 0 1 X^2+1 1 1 X^2+1 X^2+X X^2 1 X^2+X X 0 X^2 0 1 1 X^2+X X^2 X^2+X+1 X+1 1 X^2+1 X^2 X+1 X^2 X^2+X+1 X X+1 X X^2+X X^2 X^2+1 X^2 1 1 0 0 X^2 X 1 X^2+X+1 X 1 X X+1 X^2+X+1 0 X 0 0 0 0 1 1 0 1 X^2+1 X^2+X+1 X^2 X^2+X+1 0 X+1 X^2 X^2+X+1 1 X^2+1 X^2+X 0 X X X^2+1 X^2+1 X^2+X X+1 0 X^2 1 1 X+1 0 1 X^2+1 X^2+1 1 X 0 X^2 X X^2+X+1 X 1 1 X^2+X X X^2 X^2 X+1 X^2+1 1 X+1 1 X^2+X 1 X+1 0 X^2+X+1 X^2+X+1 X^2 X^2+X+1 X^2 X 0 1 X 0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 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 0 0 0 0 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 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+96x^56+202x^57+796x^58+622x^59+1671x^60+1298x^61+2396x^62+1822x^63+3361x^64+2158x^65+3756x^66+2346x^67+3545x^68+1860x^69+2599x^70+1150x^71+1325x^72+560x^73+637x^74+184x^75+228x^76+56x^77+47x^78+20x^79+11x^80+8x^81+7x^82+2x^85+2x^86+2x^88 The gray image is a linear code over GF(2) with n=264, k=15 and d=112. This code was found by Heurico 1.16 in 41.4 seconds.