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 1 1 1 1 1 1 1 1 1 0 X 0 0 0 0 0 0 X X a^4*X X a^4*X a^2*X a^6*X a^4*X a^5*X a^3*X a^4*X a^2*X a^2*X a*X a^4*X a^5*X a^3*X a*X a^2*X a^5*X a*X a^5*X a^6*X X a^2*X 0 X a*X a^3*X 0 0 a^3*X a^5*X a^2*X X a^2*X X 0 a^6*X a^3*X a^4*X a^6*X X X a^6*X a^6*X X 0 X a^6*X a^2*X a^3*X a*X a^2*X a^3*X a^6*X X a^5*X 0 a^5*X X a^2*X X a^3*X a^6*X 0 0 0 X 0 0 X X a*X a^6*X a^2*X a^5*X a^5*X a^3*X 0 X a*X 0 a^3*X a^4*X a^6*X X a^5*X X X a^5*X a^3*X 0 a^2*X a^6*X a^5*X a^4*X a^3*X a*X a^2*X a^5*X a^6*X 0 a^6*X X a^3*X a^4*X a^2*X 0 a^5*X a^4*X 0 a^2*X a^6*X a^2*X a^2*X a^2*X a*X X a*X a^6*X a^2*X a^5*X a^4*X a*X X a^3*X 0 0 a^2*X a^6*X X 0 a^2*X a^6*X 0 a^3*X 0 a^5*X X 0 0 0 X 0 a^6*X a^5*X a*X X a^3*X X X a^2*X a^4*X a^4*X a^6*X a^5*X X X a^2*X a^6*X a^5*X a*X 0 a*X a^4*X a^4*X a^3*X a*X a*X a^3*X a^6*X a*X a^2*X X X a^3*X a*X a^6*X a*X a^3*X a^4*X a^2*X X 0 a^5*X a^2*X a^6*X a*X 0 X a^4*X a^6*X 0 a^2*X a*X 0 a*X a^3*X a*X a^4*X a^5*X X a^6*X a^6*X a^6*X a^3*X 0 a*X X a^3*X X a^5*X 0 0 0 0 0 X X a^4*X a^4*X X X a^5*X a^4*X X a^6*X 0 a^3*X a*X a^3*X a^5*X a^3*X a^3*X a^6*X a^3*X a^3*X X 0 X a^4*X X 0 0 X a*X 0 a^5*X a^2*X a^2*X a*X a^2*X X 0 0 a^6*X a^4*X a*X a^2*X a^3*X a^6*X X a^6*X a^2*X a*X a^6*X a^4*X a^4*X a*X 0 a^3*X a^2*X a^5*X a^3*X a^3*X a^2*X a^2*X 0 a^2*X a*X a^5*X a^4*X 0 0 a^6*X a^4*X a^5*X generates a code of length 74 over F8[X]/(X^2) who´s minimum homogenous weight is 472. Homogenous weight enumerator: w(x)=1x^0+525x^472+1792x^480+2562x^488+3087x^496+3542x^504+28672x^511+3710x^512+200704x^519+3941x^520+4032x^528+3451x^536+2933x^544+1925x^552+875x^560+280x^568+98x^576+14x^584 The gray image is a linear code over GF(8) with n=592, k=6 and d=472. This code was found by Heurico 1.16 in 48.5 seconds.