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 X^3 1 1 1 1 1 1 1 1 0 1 1 1 X 1 X^2 1 1 1 0 X 0 X^2+X X^2 X^3+X^2+X X^3+X^2 X 0 X^2+X X^3+X^2 X^3+X X^2+X X^3 X X^3+X^2 X^3 X^2+X X^2 X^3+X 0 X^3+X^2+X X X^3+X^2 X^3 X^3+X^2+X X^3+X^2 X X^3+X^2 X X^3 X^3+X^2+X 0 X^2+X 0 X^2+X X^2 X X^3+X^2 X^3+X 0 X^2+X 0 X^2+X X^2 X X^2 X X^3+X^2 X^3+X X^3+X^2 X^3+X X^3+X^2 X^3+X X^2 X 0 X^3 X^2+X X^3+X^2+X X^3 0 X^3+X^2+X X^2+X X^3 0 X^3 X^3 0 X^2+X X^3+X^2+X X^3+X^2+X X^2+X X 0 X^3+X^2+X X^3+X^2 X^3+X^2+X X^3+X^2+X X^2 X X^3+X X^3+X 0 0 X^3+X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^3 X^3 X^3 X^3+X^2 X^2 X^2 X^3+X^2 0 0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 0 0 0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 0 X^2 X^3+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^2 0 X^3 X^3 X^2 X^2 X^3 X^2 X^3 X^2 X^3 X^2 0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 0 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 0 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 0 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 X^3 0 0 X^3 0 0 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 0 0 X^3 0 X^3 0 X^3 X^3 0 0 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 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+28x^78+92x^79+137x^80+252x^81+443x^82+344x^83+304x^84+176x^85+63x^86+100x^87+38x^88+52x^89+9x^90+8x^91+1x^158 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 0.953 seconds.