The generator matrix 1 0 1 1 1 X^2+X 1 X^3+X^2 1 1 1 X^3+X 1 1 X^3 1 X^3+X^2+X 1 1 1 X^2 1 1 X 1 1 0 1 X^2+X 1 1 0 1 1 X^2+X 1 1 X 1 1 X^2 1 1 X^2 1 1 X X 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^3+X^2 1 1 X^3+X 1 1 X^3 1 1 X^3+X 1 X^2 1 1 0 1 X+1 X^2+X X^2+1 1 X^3+1 1 X^3+X^2 X+1 X^3+X 1 X^3+X^2+X+1 X^3 1 X^3+X^2+X 1 X^3+X^2+1 X^2+X+1 X^2 1 X 1 1 0 X+1 1 X^2+X 1 X^3+X^2+X+1 X^3+X^2+1 1 0 X 1 X^3+X+1 1 1 X^2 X^2+X 1 X^3+X^2+X+1 X^2 1 X^2+1 X X 1 X^3+1 X X^2+1 X^2+X+1 1 X^3+X^2+X+1 X^2+1 X^3+1 X^3+X^2+X+1 X^2+X+1 1 X^3+X+1 X^2+1 X^3+X^2+X+1 X^2+1 X^3+X+1 X^2+X+1 X^3+1 X^2+1 X^3+X^2+X+1 0 1 X^3+1 X^2+X 1 X^2+X X^2 X X^2+X+1 X^2 1 X 1 X^3+1 X^3+1 0 0 X^2 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 0 X^3 0 0 0 X^3 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 0 0 X^3 0 X^3+X^2 0 X^3 X^3 X^3+X^2 X^3 X^2 0 0 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^3 X^2 X^3+X^2 0 X^3+X^2 X^3 0 0 X^3 X^3 X^2 0 0 X^3 X^3+X^2 X^2 0 X^3+X^2 X^3 X^3+X^2 0 X^2 0 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 0 0 0 0 0 0 X^3 0 0 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 0 0 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 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+133x^78+236x^79+615x^80+360x^81+653x^82+380x^83+512x^84+336x^85+414x^86+196x^87+139x^88+8x^89+71x^90+20x^91+5x^92+7x^94+6x^96+2x^98+1x^116+1x^120 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 0.89 seconds.