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 1 1 1 1 1 1 1 1 1 1 X 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^6*X a*X a^6*X a*X X X a^4*X a^2*X a^2*X a^5*X 0 a^4*X a^6*X a^6*X a^6*X a^6*X a^6*X a^4*X a*X 0 a^2*X X a^4*X a^4*X X a^5*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 X a^5*X a^2*X a^2*X a^3*X a*X X a*X a^2*X X a^4*X 0 0 a*X a^4*X 0 a*X a*X a^3*X a^5*X a^6*X a*X a^2*X a^2*X a*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 X a^3*X a^3*X a*X a^5*X a^2*X a^6*X X a^4*X a^5*X a^5*X a^5*X 0 a^5*X a^5*X a*X a^3*X a^2*X a^6*X a^6*X a^2*X a^2*X a^3*X a^2*X a*X a*X generates a code of length 93 over F8[X]/(X^2) who´s minimum homogenous weight is 624. Homogenous weight enumerator: w(x)=1x^0+483x^624+812x^632+672x^640+3584x^644+581x^648+25088x^652+406x^656+273x^664+252x^672+154x^680+161x^688+105x^696+70x^704+63x^712+28x^720+28x^728+7x^736 The gray image is a linear code over GF(8) with n=744, k=5 and d=624. This code was found by Heurico 1.16 in 1.13 seconds.