The generator matrix 1 0 0 0 0 1 1 1 0 1 1 1 1 X X^2+X 0 1 X X X^2 1 1 1 X 1 1 1 X^2+X X^2+X X X^2 1 1 1 1 0 1 X^2 1 0 1 1 X 1 X^2+X X^2+X 1 1 X^2+X X X^2 1 1 1 X^2+X X X^2 X 1 1 X^2 X 1 1 X^2 1 1 1 X 1 1 1 1 X^2 0 1 0 0 0 0 0 0 X^2 1 1 X^2+1 1 1 1 1 X^2+X X^2+X 1 X X X^2+X+1 1 X^2+X 1 0 X+1 1 1 1 1 X^2 X+1 1 X+1 1 0 X^2+X X^2 X^2+X 1 X^2 X^2+X X^2+X 1 X^2+X 1 X^2+X 1 X^2 X X X+1 0 0 1 1 X^2 X^2 X X 1 X^2+1 X+1 X X^2+1 0 1 X X^2+X+1 X^2+X+1 X^2+1 X^2+X+1 1 0 0 1 0 0 0 1 1 1 1 X^2+1 X^2 X X^2+1 X^2+1 X^2 X^2 0 X^2+X+1 1 1 X+1 X^2+X 1 X^2+X+1 0 X^2 X^2+1 X X^2+X 1 1 X X+1 X^2+X X+1 X X X^2 1 0 X^2+X+1 1 X^2+X+1 X^2+X 1 X^2+X+1 0 X^2+X X^2+X 1 1 X^2 X^2+X+1 1 X+1 X^2 1 X 1 1 X+1 X^2+X X^2+1 X X X^2+X 0 1 X^2+X X^2+X+1 X^2+X X^2+X X^2+X+1 0 0 0 1 0 1 1 X^2 X^2+1 X^2 X^2+1 1 X^2 X+1 X^2+X X+1 X+1 1 X^2 X X X^2 X+1 X^2+1 X+1 0 0 X^2+1 0 X^2+X+1 X^2+X X^2+1 X^2 X+1 X+1 1 X^2+X+1 1 X+1 0 X^2+X X^2+1 X+1 X^2+X+1 X^2+X 1 0 X^2 X^2+1 1 X^2+X X^2 X 1 X^2+X+1 X X^2 X^2+X X+1 0 0 1 X 1 0 X+1 X^2+X X^2+X+1 X^2 X^2+X X^2 X^2+1 X^2+1 1 0 0 0 0 1 1 X^2 X^2+1 X^2+1 0 1 0 X+1 X^2 X^2+1 X^2+X+1 0 X^2+1 0 X^2+1 X^2 X^2+X+1 X^2+1 X X X+1 X^2+X X+1 X^2+1 X X+1 X+1 X^2 1 1 X+1 X^2+X X^2+X X^2+X+1 X^2 1 1 0 X^2+X X X+1 X+1 X+1 X+1 1 0 0 1 X+1 0 1 X^2+X X+1 X^2+1 1 X^2+X X^2 X^2+X X^2+X 1 0 X^2 X+1 1 X^2+1 X^2 X+1 0 X^2+1 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+403x^64+804x^65+1336x^66+1824x^67+2847x^68+3104x^69+4282x^70+4244x^71+5669x^72+5204x^73+5936x^74+5440x^75+5671x^76+4636x^77+4188x^78+3084x^79+2667x^80+1580x^81+1238x^82+616x^83+404x^84+156x^85+116x^86+24x^87+28x^88+4x^89+20x^90+6x^92+2x^94+2x^98 The gray image is a linear code over GF(2) with n=296, k=16 and d=128. This code was found by Heurico 1.13 in 240 seconds.