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^2+X 1 1 X^3+X^2 1 X^3+X 1 1 0 1 X^2+X 1 1 X^3+X^2 1 1 1 1 X^3+X^2+X 1 X^3+X 1 X 1 1 0 0 X^3 1 1 1 1 1 1 1 X^3+X 1 1 1 X^3 1 1 X^3+X X 1 1 X^2+X 1 1 X^3+X X 1 1 0 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^2 X^3+X^2+X+1 1 X^3+1 1 X^3+X X^2+X 1 X+1 1 0 X^2+1 1 X^3+X^2 X^3+X^2+X+1 X^3+X X^3+X^2+1 1 X^3+1 1 1 1 0 0 1 1 1 X^3 X+1 X^3+X+1 X^2+X X^2+X X^3+X+1 X^3+X^2+X 1 X^3+1 1 X^3 1 X^3+X^2+X X+1 1 1 X^3+X^2+X+1 X^2+X+1 1 X^3+X X^3+1 1 X^3+X X^2+1 X^3+X^2 1 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 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 0 0 0 X^3 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 0 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 X^3 0 X^3 X^3 0 0 0 X^3 0 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 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 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 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 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 X^3 0 0 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 0 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+256x^78+240x^79+500x^80+320x^81+535x^82+416x^83+533x^84+320x^85+470x^86+240x^87+241x^88+17x^90+1x^92+1x^94+1x^96+1x^102+2x^108+1x^112 The gray image is a linear code over GF(2) with n=664, k=12 and d=312. This code was found by Heurico 1.16 in 0.782 seconds.