The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 X X^2 0 X^3+X^2 0 0 0 X^2 X^3+X^2 X^2 0 0 0 0 X^2 X^3+X^2 X^2 X^3+X^2 0 X^3 X^2 X^3+X^2 X^3 0 X^3+X^2 X^2 0 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 0 X^2 X^3 X^3+X^2 X^2 X^2 X^3 0 X^3+X^2 X^3 0 X^3+X^2 X^3 X^2 X^2 0 X^2 X^2 0 X^3 X^3 X^3+X^2 X^2 X^2 X^3+X^2 0 X^3 0 X^3+X^2 X^3 X^2 X^2 0 X^3 X^2 X^3 X^2 0 0 X^3+X^2 X^3 X^3 0 X^3+X^2 X^3+X^2 X^3 X^3 0 0 X^3+X^2 X^2 0 0 X^3+X^2 0 X^2 X^2 X^3+X^2 0 X^2 0 0 X^3+X^2 X^2 X^3+X^2 0 0 0 X^3+X^2 X^3+X^2 X^3 0 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2 0 X^3 X^3+X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^2 0 X^2 X^3+X^2 0 X^2 0 X^2 X^2 X^3 X^3 0 X^2 X^3+X^2 X^3 0 X^2 X^3 0 X^2 0 X^2 X^2 X^2 0 X^3 X^2 X^3 X^2 X^3 0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 0 X^3 X^3 X^3+X^2 X^2 X^3 X^2 X^3 X^3 X^3 0 0 0 X^3+X^2 X^2 0 X^3+X^2 X^2 X^2 0 X^3+X^2 0 0 X^3+X^2 X^2 0 X^3 X^2 X^2 0 X^2 X^3 0 X^2 X^3 X^3+X^2 0 X^2 X^3 0 X^3+X^2 X^2 X^2 X^3 X^3 0 X^3+X^2 X^2 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^3 0 X^3 X^2 X^3+X^2 0 X^2 X^3 0 X^3+X^2 X^3 0 X^2 X^3+X^2 X^2 X^2 X^3+X^2 0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 0 X^2 X^2 X^3 X^2 X^3 X^3+X^2 X^3 0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 0 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 0 X^3 X^3 0 0 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 0 0 0 X^3 0 0 X^3 X^3 0 0 0 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 generates a code of length 83 over Z2[X]/(X^4) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+136x^78+54x^80+616x^82+512x^83+496x^84+152x^86+24x^88+56x^90+1x^160 The gray image is a linear code over GF(2) with n=664, k=11 and d=312. This code was found by Heurico 1.16 in 128 seconds.