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 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 1 X 1 X 1 1 1 X^2 1 0 X 0 X 0 0 X X 0 0 X X 0 X X 0 0 0 X^2+X X^2+X X^2 X^2 X X^2+X X X^2 0 X 0 X X^2 X^2+X 0 X^2+X X^2 X^2+X X^2 X^2+X X^2 X 0 X X^2+X X^2 X^2+X X^2 X^2+X 0 0 X^2+X 0 X^2 X^2+X X^2 X X^2+X 0 X X^2 0 X^2 X^2+X X X^2+X X^2+X X^2 X^2 X^2+X 0 X^2+X X^2 0 X^2+X X^2 X^2+X 0 X^2+X X^2+X X^2+X X^2+X X^2+X X X 0 0 X X 0 X^2+X X 0 X^2+X 0 X 0 0 X 0 X^2+X X^2+X 0 X^2+X X^2 0 X^2+X X X^2 X^2+X X^2+X X^2 0 0 X^2+X X^2+X X^2 X^2 X^2+X X^2+X 0 X X^2 0 X^2+X X X^2 X 0 X^2+X X 0 X^2 X^2 X^2 X^2+X X^2 0 X X X X^2 0 X^2 X X X^2+X X^2+X 0 0 X^2 X^2+X X^2+X X^2 X^2+X 0 X^2+X X X^2+X X X^2+X X X^2 X^2+X 0 X^2 X X 0 0 0 X^2 0 0 X^2 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 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 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 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+138x^78+86x^80+274x^82+336x^84+94x^86+24x^88+70x^90+1x^160 The gray image is a linear code over GF(2) with n=332, k=10 and d=156. This code was found by Heurico 1.16 in 3.78 seconds.