The generator matrix 1 0 0 1 1 1 0 X^3+X^2 X^3+X^2 X^3+X^2 1 1 1 1 X^2+X 1 X^2+X 1 1 1 X 1 1 X X^3+X^2+X X^2+X 1 1 X^3+X X^3+X^2+X X 1 X^2 1 1 1 1 1 X^2 X 1 1 0 1 1 X^2 X^3 1 X^2+X 1 0 X X^3+X^2+X 1 1 1 X^3 0 1 1 1 1 X^3 X 1 X^2 1 1 X^2+X 1 1 1 1 1 X^3+X^2+X X^3+X^2+X 0 1 0 X 1 1 1 0 1 0 0 X^2+1 X^3+X^2+1 1 X 1 1 X^3+X^2 X^2 X^3+X^2+1 X^3+X^2+1 X^3+X^2 X+1 1 X^2+X X^3+X^2+X+1 X^3+X 1 X X^2+X 1 1 X X+1 X^3+X+1 X^2 1 1 X^3 1 X^3+X^2+X X^2+X X^2+X+1 X^3+X+1 X^3+1 1 X^3 X^3 X^2 X^3+X^2+X X^2+X+1 X^3+X^2 1 0 X^3+1 1 X^3+X^2+1 1 1 1 X^2+1 X+1 X^3+X^2+X+1 1 X^3+X^2+X X^2+X+1 X+1 X^3+1 X^3+X^2+X 1 1 X^3 1 X^2 X^2+X+1 1 0 X^3+X^2+X+1 X^3+X X^3+X+1 X^3+X^2+X 1 1 1 X^2+X+1 1 X^3 1 X^2 X^3 0 0 1 X+1 X^2+X+1 X^2 X^2+X+1 1 X X^3+1 X X^3+X^2+1 1 X^2+X 1 X^2+X X^2+1 1 X+1 X^3+X X^3+X X^2 X^3+X^2+X+1 X^2 X^3+X+1 1 1 X^2 1 X^3+X^2+X X^2+X+1 X^3+X^2+1 X^2+X+1 X^3+X^2+1 0 X^2+X X^3+X^2+X+1 X^3+X+1 X^3+X+1 1 X X+1 1 X^3 X^3 X^3+1 1 X^3+1 X^3+X^2+1 X^3 X^2+X 0 X X^3+X^2+X X^3+X^2+1 X^3+X^2 0 1 X+1 X^2+1 X+1 X^3+X^2+X X+1 X^3 X^2+1 X^3 X^3+X+1 X^3 X^3+X^2 X^2+X X^2+1 X^3+X^2 X^2+1 X^3+X 1 X^3+X^2+1 X^2+1 X^3+X^2+X+1 X^2 1 X+1 X^3+X^2+X+1 0 0 0 0 X^2 X^2 0 X^2 X^3+X^2 X^2 X^3 X^2 0 X^3 X^3+X^2 X^3+X^2 0 X^2 X^2 0 0 X^3 X^3+X^2 0 X^2 X^3 X^3 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^3+X^2 0 0 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 0 0 X^2 0 X^2 0 X^3 X^3 0 X^3 X^3 X^3 X^2 X^3+X^2 0 X^3+X^2 0 X^3 X^3+X^2 0 0 X^2 X^3 0 X^2 X^2 X^3+X^2 X^2 X^2 X^2 X^2 generates a code of length 83 over Z2[X]/(X^4) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+126x^77+851x^78+1236x^79+1862x^80+1650x^81+2014x^82+1854x^83+1821x^84+1238x^85+1373x^86+906x^87+749x^88+274x^89+206x^90+96x^91+64x^92+24x^93+11x^94+18x^95+6x^96+2x^99+1x^100+1x^102 The gray image is a linear code over GF(2) with n=664, k=14 and d=308. This code was found by Heurico 1.16 in 9.11 seconds.