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 1 1 1 1 1 1 1 1 X X 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 0 X 0 0 X X a*X a^2*X a^4*X a^5*X a^5*X X a^5*X a^6*X 0 a*X a^5*X a*X a^5*X 0 a^4*X a*X a*X a^2*X a*X X a^4*X a^2*X X a^3*X a^6*X a^4*X 0 0 a^4*X a^2*X a^2*X a^6*X a^2*X a^3*X a^2*X a^5*X a^2*X a^5*X a^6*X a^4*X a*X a^4*X X a^4*X X a^5*X a*X X a^3*X X 0 a^2*X a^2*X a^5*X a*X a*X a^4*X a^3*X a^4*X a^2*X a^6*X a^3*X a^3*X a*X X a*X a^4*X a^4*X 0 0 a^5*X a^5*X a^5*X a*X a^4*X X X a^2*X X a*X a^3*X a^2*X a^4*X a^4*X X X a^5*X a*X a^3*X a^6*X a^2*X X 0 0 X 0 a^6*X a^5*X a*X a^6*X a^6*X a*X a^6*X a^2*X a*X a^3*X X a^5*X X X a^4*X a^3*X X a*X a^4*X 0 a^2*X 0 0 a^2*X a^2*X a^6*X X a^5*X a^4*X a^6*X X a^2*X 0 a^6*X a^2*X a^5*X X a^2*X a^6*X a^5*X a^4*X a^5*X a^4*X a*X a^5*X 0 a^6*X a^2*X X 0 a^3*X a^3*X a*X a^4*X a^4*X a^4*X a^5*X a^4*X 0 a^3*X a^3*X a^6*X a^4*X a^6*X a*X X a^6*X a^5*X a^4*X a^4*X a*X X a^2*X a*X X a^2*X a^4*X a^6*X a^6*X a^5*X a*X a^2*X a*X a^5*X a*X a*X a^5*X a^2*X a^3*X a*X 0 a^3*X X a^3*X 0 0 0 X X a^4*X a^4*X X a^6*X a^4*X a^6*X a^6*X a^3*X a*X a^4*X a*X a^3*X a^5*X a^6*X a^2*X a^4*X X 0 a^5*X 0 a^5*X a*X a^6*X a^3*X 0 a^3*X a^6*X a^3*X a^4*X a^2*X a*X 0 a^4*X a^2*X X a^2*X a^3*X 0 a^5*X a^3*X a^5*X a^2*X a^5*X a^3*X a^4*X a^6*X 0 a^2*X a*X a^2*X X a^3*X a*X a^6*X a^4*X a^3*X a^3*X a^5*X a^5*X a^4*X a*X a^4*X a^5*X 0 a^3*X a^5*X a^2*X a^5*X 0 a^2*X a^5*X a^5*X a^6*X 0 a*X a^2*X a^2*X a*X a^5*X a^4*X a^4*X a*X a^4*X a^6*X a^2*X a*X X X 0 a*X a^6*X a^4*X a^5*X generates a code of length 98 over F8[X]/(X^2) who´s minimum homogenous weight is 656. Homogenous weight enumerator: w(x)=1x^0+245x^656+777x^664+56x^665+721x^672+1176x^673+623x^680+8232x^681+469x^688+19208x^689+280x^696+196x^704+294x^712+147x^720+119x^728+49x^736+70x^744+63x^752+14x^760+21x^768+7x^776 The gray image is a linear code over GF(8) with n=784, k=5 and d=656. This code was found by Heurico 1.16 in 1.22 seconds.