The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a^6*X 1 1 1 1 1 1 1 1 1 1 1 a^2*X X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 a^5*X 1 a^5*X 1 X 1 1 1 a^4*X 1 1 1 1 1 1 1 1 1 1 1 a^6*X 1 a^5*X 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 a a^2 a^6*X+a^3 a^6*X+a^4 a^5 a^6 a^6*X a^6*X+1 X+a X+a^2 1 a^6*X+a^5 X a^5*X+1 a^5*X+a^3 a^6*X+a^2 a^4 a^6*X+a^6 a^4*X+a a*X+a^3 a^5*X+a^6 X+a^5 1 1 X+a^4 a^2*X a^4*X+a^2 a^2*X+a^5 a^5*X+a^6 a^4*X+a^3 a^2*X+1 a*X+a a^3*X+1 a*X+a^5 a*X X+a^3 a^6*X+a^6 a^2*X+a^4 a^4*X+a^6 a^4*X+1 a^3 a*X+a^4 1 a^4*X+1 1 X+a 1 X+a^4 a a^3*X+a 1 a^3*X+a^5 1 a^6*X+a^5 a^2*X+a^2 a^4*X+a^4 a^6*X+a^3 a^6*X+1 X+a^6 a^3*X+a^6 a^5*X+a^3 a^6*X+a^4 1 X+1 1 a^2*X+a^6 a^4*X+a^5 a^2*X+a^5 a^3*X+a^3 a*X+a^4 1 a^5*X+a^4 a*X+a^3 a^6*X+a^5 a*X+a^5 a^4*X+a^3 X+1 X+a^6 a^2*X+a^3 a^2*X 0 0 1 a^6 a a^4 1 a^5 a^3 a^2 a^3*X+1 a*X+a^5 a^6*X a^5*X+a^2 X+a^6 X+1 a^5*X+a^3 a^6*X+a a^5*X+a^6 a^5*X a^6*X+a^6 a^2*X+a^5 a^2*X+a^4 X+a a^4*X+a^3 a^3*X+a^2 a^4*X+a a^4*X+a^5 a*X+a^4 X+a^2 a^2*X+a^6 a^4*X+a^5 a^2*X+a X+a^4 a^5*X+a^4 a^2*X+1 a^2*X+a^2 a^6*X+a^4 X+a^6 X a*X+1 a^6*X+a^2 0 a*X a^3*X+a a^4*X+a X+a^6 a^4*X+a^6 X+a^3 a^5*X+a^5 a*X+a^2 a^5*X X+a^3 a*X+a^6 a a^6*X+a^2 a^2*X+a a*X+a a^6*X a^4*X+a^6 X+a^2 X a^6*X+a^4 a^5*X+a^2 a^4*X+a^3 a^5*X+1 a^3*X+a^2 a*X+a^6 a^6 a a^6 a^4*X a^5*X+a a^5*X+a^4 a^2*X+a a^3*X+a^3 a^5 a^2 a^4*X+a^5 a^4*X a^4 a^6*X+1 a*X+a^4 a*X+1 generates a code of length 84 over F8[X]/(X^2) who´s minimum homogenous weight is 568. Homogenous weight enumerator: w(x)=1x^0+3073x^568+2072x^569+448x^570+560x^571+2016x^572+840x^573+2128x^574+8120x^575+17766x^576+5096x^577+3920x^578+2912x^579+6328x^580+3248x^581+5656x^582+13160x^583+25627x^584+7112x^585+6944x^586+5040x^587+9968x^588+3080x^589+4704x^590+13384x^591+23891x^592+8792x^593+10192x^594+5824x^595+10360x^596+3584x^597+5432x^598+11928x^599+23205x^600+5600x^601+56x^608+28x^616+42x^624+7x^632 The gray image is a linear code over GF(8) with n=672, k=6 and d=568. This code was found by Heurico 1.16 in 18 seconds.