The generator matrix 1 0 1 1 1 X^2+X 1 1 X^3+X^2 1 X^3+X 1 1 1 0 1 1 X^2+X 1 1 X^3+X^2 1 1 X^3+X 1 1 0 1 1 X^3+X 1 1 X^2+X 1 X^3+X^2 1 1 1 0 1 1 X^2+X 1 1 X^3+X^2 1 1 X^3+X 1 X 1 X 1 1 1 1 1 1 1 1 X 1 X X X 1 1 1 1 0 X^3 0 1 1 1 1 1 X^3+X^2 1 1 X^3+X^2 1 0 1 X+1 X^2+X X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+X 1 X^3+1 X+1 0 1 X^2+X X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+X X^3+1 1 0 X+1 1 X^2+X X^2+1 1 X^3+X X^3+1 1 X^3+X^2+X+1 1 X^3+X^2 X^2+X X+1 1 0 X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+X X^3+1 1 0 X^3+X^2 X^3 X^2 X^2+X X X^3+X^2+X X^3 X^2 X^2+X X 0 0 X^3+X^2+X X^2 X^2+X X^3+X^2+X X^2+1 X^3+1 X^2+X+1 X+1 X X 1 1 X+1 X^3+X+1 X^3 X^2+X+1 1 X^2+X+1 X^2+X+1 X 0 0 0 X^3 0 0 0 0 0 0 0 0 0 0 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 X^3 X^3 X^3 0 0 X^3 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 0 X^3 0 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 0 0 0 X^3 0 0 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 0 0 0 0 0 0 0 0 0 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 0 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 0 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 0 X^3 0 generates a code of length 82 over Z2[X]/(X^4) who´s minimum homogenous weight is 76. Homogenous weight enumerator: w(x)=1x^0+6x^76+242x^77+208x^78+638x^79+156x^80+734x^81+315x^82+652x^83+148x^84+514x^85+156x^86+224x^87+6x^88+42x^89+21x^90+20x^91+2x^92+4x^93+2x^94+2x^95+1x^96+1x^110+1x^134 The gray image is a linear code over GF(2) with n=656, k=12 and d=304. This code was found by Heurico 1.16 in 0.656 seconds.