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 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^2 X^3 X^3 X^2 X^3 X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 X^2 0 X^3+X^2 X^3+X^2 X^2 X^2 0 X^3 X^3+X^2 X^3+X^2 0 0 X^3 0 0 0 X^3 0 0 0 0 0 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 X^3 X^3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 0 0 0 X^3 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 0 0 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 0 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 0 generates a code of length 81 over Z2[X]/(X^4) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+32x^77+16x^78+126x^80+704x^81+96x^82+32x^85+16x^86+1x^160 The gray image is a linear code over GF(2) with n=648, k=10 and d=308. This code was found by Heurico 1.16 in 0.954 seconds.