The generator matrix 1 0 0 0 1 1 1 X 1 X^2+X 1 X^3+X X^3+X^2 1 1 X^3+X^2+X X 1 1 1 X^3 1 X^3+X X^3+X^2+X X 1 1 1 1 X X^3+X 1 X^2+X X 1 X^3+X 1 1 X^3 X^3+X^2 1 X^2+X X^2+X 1 X^3+X 1 X^3+X^2+X 1 X^3+X^2 X^2+X 1 1 1 1 X^2+X 1 X^2 0 1 1 1 X^3+X^2 1 X^3+X^2 X 1 0 X^2 X^2 1 1 1 1 X^2 X^2 X^3+X^2 1 0 1 0 0 X^3 X^3+X^2+1 X^3+X+1 1 X^2 X^2 X^2 1 1 1 X^3+X+1 X^3+X 1 X^2+X+1 X^3+1 X^3+X^2+X+1 1 X^3+X^2 X^2 1 X^2+X X^3+X X^3+X^2+X X^3+X^2 X^3+1 1 X X^2+X+1 1 1 X^2 X^3+X^2+X X^3+X^2+X+1 1 X^3+X 1 X^3+X^2 X^2+X 1 X^3+1 1 X^3+X^2+1 1 X^3+1 X^3+X^2+X 1 X^3+X 0 X+1 1 1 X^3+X^2+X 1 1 X^3+X^2+X X+1 X^2+X X^2 X^2+X+1 1 1 X^3+X^2+1 1 X^2+X 1 X^2 X^3+X X^3+X X^2 1 1 1 X^3+X^2 0 0 1 0 X^3+X^2 X^3 X^2 X^2 1 1 X^3+X+1 X^3+X+1 X^3+X+1 X+1 X^3+1 1 X^2+X X^2+X+1 X^3+X^2+1 X^2+X 1 X 1 X^2 X^3+X^2 X^3+X+1 1 X^3 X^3+X^2+X 1 1 X X+1 X^2+1 X^3+X X^2+X X+1 X^3+X^2+1 1 0 X^2 1 X^2+1 X^3+X^2+X+1 X^3+X^2+X X^2+X X^3+X+1 X^2+X+1 X^3+X^2+X X X^3 X^2+1 X^3+X^2+X X^3+X^2 X^2 X^2+X+1 X^2+X+1 X^2 X^2+1 X^3+X^2 X^2+1 1 X^2+1 X^2+X+1 0 X^3+X^2 X^3+X^2+1 1 X^3+1 X^3+X^2+X+1 X^2+X X^3+1 X X+1 X^3+X^2+1 X^2+X X^2 0 0 0 1 X^2+X+1 X^3+X^2+X+1 X^3 X+1 X^3+X+1 X^3+X^2+X+1 0 X^3+X^2+1 X^2+X X^3+1 X^3+X^2+X X^3+X X^2+X X+1 0 X^3+X^2+1 1 X^3+X^2 1 1 1 X^3+X^2 X^3+1 X^3+1 X+1 X^2 0 X^2 X X^3+1 1 1 X^3+X^2+X X+1 X^2+1 X^2+1 X^2+X X^3+1 X^3+X^2+X+1 X^2+X+1 X^2+X+1 X^3+X X^3+X^2 X^2+X 1 X^3 X^3 X^3+X^2+X X^2+X+1 X^3+X^2+1 X^2+X X+1 0 X^2+X+1 X^2 X X^2+X X^3+1 1 X^2 X^3+X^2+X+1 X^2+1 X^3+X^2 X^2+X X^2 X X^3+1 X^2+X+1 X^3+X^2+X X^2+1 X^3+X^2+X+1 X X 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+316x^70+1458x^71+2834x^72+4612x^73+5626x^74+7000x^75+7100x^76+8292x^77+7499x^78+6666x^79+5364x^80+3864x^81+2254x^82+1496x^83+618x^84+332x^85+107x^86+56x^87+19x^88+4x^89+6x^90+12x^91 The gray image is a linear code over GF(2) with n=616, k=16 and d=280. This code was found by Heurico 1.16 in 40.3 seconds.