The generator matrix 1 0 0 0 1 1 1 1 X^3 1 X^3+X X^2+X X^3+X^2+X 1 1 0 1 1 1 1 X^3+X^2 1 1 X^3+X^2 1 X^2+X 1 X^3+X^2+X X^2+X 1 X^2 X^3 X^3 1 1 X^2 0 1 X^3+X^2+X 1 1 1 X^3+X^2+X 1 X^3+X^2+X 1 1 X^3+X^2 1 X^3 1 X^2 X^3+X^2+X 1 X^3 X^2 1 1 X^2+X X^3+X^2+X X^3+X^2+X 1 X 0 1 X^2+X X^3+X^2 X^3+X^2+X 1 X 1 0 1 0 0 X X^2+1 X^3+X^2+X X^3+X^2+1 1 X^2+1 1 1 X^3+X X^3+X^2 1 X^2+X X^3+X^2+X+1 X 0 X^3+X+1 1 X^2+X+1 0 X^3+X^2 X^3+1 X^2+X X^3 1 1 X^2+X X 1 1 X^2+X+1 X^3+1 1 X^3+X^2 X^2+X 1 X^3+X^2+X X^2 X^3+X^2+1 X^3 X^3+X^2 1 X^2+X X^2+X+1 1 0 X^2+X X^3+X^2 1 X^3 X^3+1 1 1 X^3+X^2+X 1 1 X^3+X X^2 X^3+X+1 1 X^3+X X^3 1 X^2 X^2 X^3+X^2+1 1 0 0 0 1 0 0 X^3 X^3+X+1 X+1 X^3+1 X^2+1 X+1 X^2 1 1 0 X^3 X^3+X^2+X X^2+1 X^2+X+1 X^3+X^2 1 X^2+X+1 X^3+X 1 X^3+X^2+1 1 X^3+X+1 X^2 X^3+X^2+X X^3+X 1 X^2+X+1 X^2+X X^3+X^2+1 X^3+X^2 X^2+X+1 1 X^3+1 X^3+X X^2 0 X^3+X^2+X X^2 X+1 1 X^2+X X^3+X^2+X+1 X+1 X^2+1 1 X^3+X^2+1 X^3+X^2+X X^3+X X^3+X^2+X+1 X^3+1 X^2 X^2+X+1 1 X^3+X+1 1 1 X^2 X^3 X^3+X^2+X 1 X^3+X^2+1 1 X X^3 X^2 0 0 0 0 1 1 X^3+X+1 X+1 X^3+1 X X^3 X^3+X^2+X+1 X^3+1 X^3+X+1 X^3+X^2+X X^3+X 1 0 X^3+X^2 X+1 X^2+X+1 1 X^3+X X^3+X X^3+X^2+X+1 X^2+1 X^3 X^3+X^2+1 X^2 X^2+1 X^3+1 X^3+X+1 X^3+X^2+X+1 1 X+1 X^3+1 X^3 X^2+X X^2 X^2+X X^3+X^2+X+1 X^3+X X^2+X 1 X^3+X^2+X X^3+X^2+1 0 0 X^2+X X^3+1 X^3 X^2+X+1 X^2 1 X X^2 X^3+X+1 0 X^3 X^3+X X+1 X^3+1 X^3+1 1 1 0 X^2 X+1 1 X X^2+X X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 0 X^3 0 0 X^3 generates a code of length 71 over Z2[X]/(X^4) who´s minimum homogenous weight is 63. Homogenous weight enumerator: w(x)=1x^0+188x^63+1187x^64+2836x^65+4625x^66+7662x^67+10240x^68+13398x^69+16474x^70+17124x^71+17177x^72+14166x^73+10557x^74+7374x^75+3868x^76+2224x^77+1148x^78+452x^79+213x^80+92x^81+26x^82+16x^83+18x^84+2x^85+2x^89+2x^90 The gray image is a linear code over GF(2) with n=568, k=17 and d=252. This code was found by Heurico 1.16 in 160 seconds.