The generator matrix 1 0 0 1 1 1 X X^3+X 1 1 1 0 1 X^3 X^2 1 1 1 1 X^2+X X^3+X X^2 X^3+X^2+X 1 1 1 X^3 1 X^3+X^2+X 1 X^3+X 1 1 1 X^3+X^2 1 1 X^3+X^2+X 1 1 X 1 1 1 X^3 X^2+X X 1 1 1 1 1 X^3+X^2 1 1 1 X^2 1 X^3+X^2+X 1 1 1 X^2 1 1 1 X^3+X 1 0 1 X^3+X^2+X 1 1 X^3 X^2 1 1 0 1 0 0 X^2+1 X+1 1 X^3 0 X^3 X^3+X+1 1 1 1 X^2+X X^2+1 X^3+X^2+X+1 X^3+X X^3+X^2 1 1 X^3+X^2+X 1 X^2 X+1 X^3+X 1 X^3+X^2+X+1 X X 1 X+1 X^2+1 X^3+X^2+X+1 1 X^3+X+1 0 1 X^3+1 X^3+X^2 X X^2 X^3+1 1 1 1 1 1 X+1 X^3+X^2+1 X^2+X X^3+X^2 1 X^3+X^2+X 1 X^3+X^2+1 X^3+X^2+X X+1 X^3 X 0 X^3+1 1 X^3+X X^2+X+1 X^3+X+1 1 X 1 X 1 X^3+X X^3 X^2 1 X^3+X^2+X+1 0 0 0 1 1 1 0 X^2+1 1 X^3+X X^2+X+1 X^2+1 X X^2+X X^3+X^2+1 1 X^3+X^2 X^3+X+1 X^2+X X^3+X+1 X^3+X+1 X^2+X 1 X^3+X^2+1 X^3+X 0 1 X^3+X^2 X^3+X^2+X+1 1 X^2 X^2 X^2+X 0 X^3+X+1 X^3+X^2+X+1 X^3 0 X^2 X^3+X^2+X+1 1 1 X^3+X^2+1 X^3+1 X^3+X^2+X X+1 X^3+X X^3+X^2+X X^3+X^2+X+1 X^3+X^2+X+1 X^3+X^2+X X^3+X X^3+X X^2+1 X^3+X+1 X^3+X^2 X 1 X^2+X 1 X^3+X+1 X^3+X^2 X^2+X+1 X^3+X X^3+X^2+X X^3+X X^2+X+1 X^3+X+1 1 X^3+X^2+X+1 X^3+1 X^2+X X^2+X X^3+X+1 1 X^3+X X^3+X^2+X+1 X^2 0 0 0 X X^3+X X^3 X^3+X X^3+X X^2+X X^3+X^2+X X^3+X X^3+X^2 X^2 X^3+X X X^3 X^3+X^2+X 0 X^3+X^2 X^3+X^2 X^3+X^2+X X^2 X^3 X^3 X X^2+X X^3+X^2+X X^3+X^2 0 X^3+X^2+X X^2 X^3+X^2+X X^3+X^2+X 0 X^3+X X^2 X^3+X^2 X^3+X X^2+X X^3 X^2+X X^3+X^2+X X^3+X^2 X X^2 X X^3 0 0 X^3+X^2+X X X^3+X X^3+X^2 X^2 X^2 X^2+X 0 X^3+X^2 X^2+X X X^3+X^2+X X^2 X^2+X X^2 X^3 X X X^3+X X^3 X^3+X^2 X^2 X^3+X X X^3+X^2+X X^3+X X^2 X^2 generates a code of length 77 over Z2[X]/(X^4) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+67x^70+548x^71+1661x^72+2256x^73+2774x^74+3560x^75+3927x^76+4006x^77+3709x^78+3312x^79+2579x^80+1920x^81+1199x^82+630x^83+333x^84+102x^85+100x^86+40x^87+10x^88+4x^89+23x^90+6x^91+1x^96 The gray image is a linear code over GF(2) with n=616, k=15 and d=280. This code was found by Heurico 1.16 in 16.5 seconds.