The generator matrix 1 0 0 1 1 1 X X^3+X 1 1 1 X^3+X^2 X^2+X 1 1 X^2+X 1 0 1 X 1 1 1 1 X^3 1 X^2 0 X^3+X 1 1 0 1 1 X^3+X^2+X 1 X^2+X X^2 1 1 1 1 X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X 1 1 X^2 X^3+X 1 X^3 X^3+X^2 1 1 X 0 1 X^3+X^2+X X^3+X 1 X X^3+X^2 1 1 1 1 1 1 1 X^3+X 1 X^2+X X^3+X 1 0 X^3 X^3 X^3+X^2 1 1 1 1 0 1 0 0 X^2+1 X+1 1 X^3 0 X^3 X^3+1 1 1 X+1 X^2 X^3+X X^3+X+1 1 X^3+X^2+X 1 X^3+X^2+1 X^3+X^2+X X^2+1 X^3+X^2+X+1 1 X X^3+X 1 1 X^2+1 X^2 1 0 X^2+X+1 X^2 X^2+X+1 1 0 X^2+1 X^3+X^2+X X^3+X X^3+X 1 1 X^3+X X^3+X^2+X 1 X^2+X 1 1 X^2+X+1 1 1 X^3+X^2+X X^3+X^2+1 1 1 X+1 X^2 1 X^3+X^2+X+1 1 1 X^3+X+1 X^2+X X^3+X+1 X^2 X X^3+X X^3+X+1 1 0 1 1 X^3+X^2+1 1 1 X X^3 X^2+1 1 X^3 0 0 0 1 1 1 0 X^2+1 1 X X^3+X^2+X+1 X^2+X X+1 X^3+X^2+X 1 X^3+X+1 1 X^3+X+1 X^2+X X^3+X^2 1 X^3+X^2 X^2+X X+1 X^3+X^2 X+1 X^2+1 1 X^3+X X^2+X+1 X^3+X+1 X^3+X^2+1 0 X^3+X X 1 X^3+X^2+1 0 1 X^3+X^2+X X^3 X^2+1 X^3+1 X^3+1 X^3+X 1 1 1 X^2+X X^2+X+1 X^2 X^3 X^3+X^2+1 X^3+1 X^3+X X^2 X^3+X^2+1 X^3+X+1 1 1 X^3 X^2+X X^2 X^2 X^2+1 X^2+X+1 X^3+X X^3+X^2 X^3+1 X^3+X+1 X^2 X^3+X+1 X^3+X X^2+X+1 X^3+X^2 X^3+X^2 X^3+X^2+1 X^3+X X^3+X^2+X 1 X^2+X+1 X^2 X+1 0 0 0 0 X X^3+X X^3 X^3+X X^3+X X^3+X X X^3+X^2+X X^3 X X^2 X^2 X^2+X X^2+X X^3+X X^3+X^2 X^2 X^2 X 0 X^2+X X^2+X X^2 X^3+X^2 X^3 X^2 X^3+X^2+X X^3+X^2 X^3+X^2+X 0 X^2 0 X^3+X X^3+X^2 X^3+X^2 X^3 X^2+X 0 X^3+X^2+X 0 X^3+X^2+X X^3+X X^2 0 X^3+X^2 X^3+X X^3 X^2 X^2+X X^2 X^3 X^3+X^2+X 0 X^3+X^2 X^2+X X^2+X X X^3+X^2+X X^3+X^2+X X^3+X^2 X^3+X^2 X^2+X X^3+X X^3+X X X^3 X X^3+X^2+X X^2 0 X^3+X 0 X^3+X X^2 X^3+X^2+X X^2 X^2 X X^3 X^3 generates a code of length 83 over Z2[X]/(X^4) who´s minimum homogenous weight is 76. Homogenous weight enumerator: w(x)=1x^0+152x^76+718x^77+1590x^78+2350x^79+2863x^80+3618x^81+3610x^82+3826x^83+3587x^84+3468x^85+2421x^86+1728x^87+1229x^88+822x^89+387x^90+138x^91+114x^92+74x^93+25x^94+22x^95+13x^96+4x^97+7x^98+1x^100 The gray image is a linear code over GF(2) with n=664, k=15 and d=304. This code was found by Heurico 1.16 in 17.3 seconds.