I have an exercise that asks for the minimum distance of a BCH-Code with length 63 over $F_2$ with generator polynomial given by $g(x)=(x+ 1)(x^6 +x+ 1)(x^6 +x^5 + 1)$.
As $g(x)=x^{13}+x^{11}+x^8+x^5+x^2+1$, the minimum distance is $\leq 6$.
I know that one can show that the distance is $\geq 6$ and therefore is equal to 6. Can someone help me how to do that? So show that the designed distance is 6?