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 X^3+X^2 1 1 1 1 X^3+X 1 1 0 1 1 X^3+X 1 1 X^3+X^2 1 1 X^2+X 1 1 0 1 1 X^2+X 1 1 X^3+X^2+X 1 1 X^3+X^2 1 X 1 X 1 X 1 1 1 1 1 X X X 1 X^3+X 1 X^2 X^3+X^2 X X^3+X 1 1 0 X 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 1 X^3+X^2 X^3+X^2+X+1 X^3+X X^3+1 1 0 X+1 1 X^2+X X^2+1 1 X^3+X X^3+X^2+X+1 1 X^3+X^2 X^3+1 1 0 X+1 1 X^2+X X^2+1 1 X^3 X^3+X+1 1 X^3+X^2+X X^3+1 1 X^3+X^2 0 X^3+X X^3+X^2 X X^2 X^3+X X^2+X X^3+X^2 X^3 0 X^3+X X X X+1 1 1 X X 1 1 X+1 X^3+X+1 1 X^2+X 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 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 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 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 0 0 0 0 0 X^3 0 X^3 0 0 0 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 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 X^3 0 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 0 X^3 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 0 X^3 X^3 0 0 X^3 0 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+200x^68+280x^69+400x^70+504x^71+486x^72+528x^73+360x^74+464x^75+411x^76+216x^77+128x^78+56x^79+47x^80+8x^82+4x^84+2x^88+1x^124 The gray image is a linear code over GF(2) with n=584, k=12 and d=272. This code was found by Heurico 1.16 in 120 seconds.