The generator matrix 1 0 0 1 1 1 X X^3+X 1 1 1 X^3+X^2 1 X^3+X^2+X 1 1 X^3 1 X^2 1 0 1 X^3+X X^3+X^2+X 1 X^3+X^2 1 1 X^3+X^2 1 X^3 X^2+X 1 1 1 1 1 1 0 1 X^2+X X^3+X^2+X 1 1 X^3 1 X^2 1 X X X^2 1 X X^2+X 0 1 X^3+X X^3 X^3+X^2 1 1 1 1 1 1 1 X X^3 1 1 1 1 X^2 1 X^3+X^2+X X^3 X^2+X 1 1 1 0 1 0 0 X^2+1 X+1 1 X^3 0 X^3 X^3+1 1 X^3+1 1 X^3+X^2 0 1 X^2+1 X^2+X X^3+X^2+X+1 1 X^2 1 1 X^3+X^2+1 X^2+X X^3+X^2+1 X 1 X^2+X X 1 X X^3+X^2+1 X^3+X^2+X+1 X^3+X+1 X^3+X X^3+X+1 1 X^3+X^2+X X^3+X X X^2+X+1 X^3+X 1 X^2+X+1 0 X^2+1 1 X^3+X^2 1 X^3+X X^3+X^2+X 1 1 X^2 1 1 1 X^3+X X^3+X^2+X 1 X X^3+X^2+1 X^3+X^2+X X^3+X^2+X X^3 1 X X+1 X^2 0 1 0 X^2+X 1 1 X X^3+X+1 X^2 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^2 X^3+1 X^2 X^3+X^2+X X^2+X 1 X^2+X+1 X^2+X+1 X^3+X^2+X+1 X^3+X X^2+1 X^2+1 1 X^3 X^3 X^3+X^2+X X^3+1 1 X^3+X+1 X X^3+X+1 X^3+X X^3+X^2+1 X^2+X+1 0 1 X^2 1 1 X^3+1 X^2+1 X^2+X X^2+X+1 1 X^3+X^2 X^3+X 1 X^3+X^2+X+1 X^2+1 1 X^3+X^2+1 0 X^3+X^2+X 0 X^3+X^2 X X^3+X 0 1 X^2+X+1 X^3+X^2+1 1 X^2+X 1 X^3+1 X^3+X+1 X^3+X+1 X^2+X X^3+X^2+X+1 X^2+1 X+1 1 X^2 X^3+X^2 X^3+X^2 X^2+X X^2 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^2 X^2+X X^3+X^2 X^2+X X^2 0 X^3+X^2 X^2+X X^3+X X^3 X^2+X X^3+X^2 X^3+X^2 X^3+X X^2+X X^3+X^2 X X^2 X^3 X^2 0 X^3+X X^3 0 X^3 X^3+X^2+X X^2+X X^2+X X^3+X X^3+X^2 X^3+X X 0 0 X^3+X^2+X X^2 0 0 X^2 X^2+X X^3+X^2+X 0 X^3+X^2 X^3 X^2 X^3+X^2+X X^2+X X X^3+X X^2 X X^3+X^2+X 0 X^3+X^2+X X^2+X X^3 X^3+X^2+X X^3+X^2 X^2 X^3+X^2+X X X^2 X^3+X^2 X X^3 X^2+X X^2+X 0 generates a code of length 80 over Z2[X]/(X^4) who´s minimum homogenous weight is 73. Homogenous weight enumerator: w(x)=1x^0+82x^73+736x^74+1542x^75+2233x^76+2808x^77+3550x^78+3746x^79+4161x^80+3610x^81+3471x^82+2534x^83+1815x^84+992x^85+656x^86+438x^87+200x^88+64x^89+49x^90+44x^91+22x^92+12x^93+2x^98 The gray image is a linear code over GF(2) with n=640, k=15 and d=292. This code was found by Heurico 1.16 in 17.1 seconds.