The generator matrix 1 0 0 0 1 1 1 1 X^3 1 1 X X^3+X 1 X^3+X 1 1 X^3 X^3+X^2 1 X^2+X 1 X^3+X^2 1 X^3 1 1 1 X^3+X X^2 X 1 1 X^3 X^3+X 1 X^3+X^2 1 X^2 1 X^3+X^2 1 X^3+X^2+X 1 1 1 1 X^3+X^2 1 X^2 X^3+X 1 1 X^3 0 1 X X^2 X X^3+X^2+X X^3 1 X^3+X^2+X 1 1 1 1 0 1 0 0 X X^2+1 X^2+X X^3+X^2+X+1 1 X^3+X X^3+1 1 X^3+X^2 X^3+X+1 1 X^3+X^2+X X^3+X^2+X+1 1 X^2+X X^3+X^2+1 1 X^2+X+1 1 X^3 1 X^2+1 X X^2+X X^2+X 0 1 X^3 X^3+X^2+1 0 X^3+X^2+X X^3+X+1 1 X^3+X^2+1 1 X^2 X^3+X^2 X^3+X^2 X^3 0 X X^2+X+1 X^3+X^2+1 1 X^2 1 1 1 X X^2+X X^3+X X X^3+X 1 0 1 X^3 0 X X^2+1 X^3+X+1 X^2 0 0 0 1 0 0 X^3 X^3+X+1 X+1 X^3+X+1 1 X^3+1 X^2+X+1 1 X^2 X^3+X^2 X X^2+1 1 X^3+X X^2 1 0 X^3+X^2+X 1 X^2+X X^3+X^2+X+1 X^3+X+1 X^3 1 1 X X^3+X+1 X^3+1 1 X^3 X X^3+X+1 1 X^3+X^2+X+1 X^3+X^2 X^2+X X^2+1 1 X X^3+X^2+1 X^2+X+1 X^3+X^2+X X^2+1 0 1 X^3+X^2+1 X^3+X X^3+X^2+1 X^2 1 0 1 X X^2+X X^2+X+1 1 X^2 1 X^3 X^3+X^2+X X+1 0 0 0 0 1 1 X^3+X+1 X^2+X+1 X^2+1 X X^3+X^2+X X^2 X+1 X^3+X^2+X+1 X^2+X X^2+1 X^3 X^3+1 X+1 1 X^2+1 X^2+X X^3+X^2 X^3+X^2 X+1 1 0 X^3+X^2+X X^3+X+1 X^3+X^2+X+1 X X^2 X^3+1 X^3+X^2+X+1 1 1 X X^3+X^2 X^3+X^2+1 X^2+X+1 X^2+X+1 1 X^3+X^2+1 0 X^3+1 X^3+X^2 X^3+X 1 X^2+X X^3+X^2+X X^3+X^2+X 1 X^2 X^2+1 1 X^3 X^2 X^2 X^3 1 1 X^3+X^2+1 1 X^3+X^2+1 X^3+X X^3+1 X^2 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 0 0 X^3 0 X^3 0 0 0 0 X^3 X^3 0 generates a code of length 67 over Z2[X]/(X^4) who´s minimum homogenous weight is 59. Homogenous weight enumerator: w(x)=1x^0+132x^59+1114x^60+2418x^61+4820x^62+7372x^63+10775x^64+13030x^65+17630x^66+16464x^67+17627x^68+13658x^69+10901x^70+6872x^71+4574x^72+2064x^73+954x^74+350x^75+167x^76+76x^77+29x^78+24x^79+12x^80+2x^82+2x^83+2x^84+2x^89 The gray image is a linear code over GF(2) with n=536, k=17 and d=236. This code was found by Heurico 1.16 in 149 seconds.