Any string of terminals that can be generated by the following context-free grammar, where $S$ is start nonterminal symbol

$S\to XY$

$X\to 0X\mid 1X\mid 0$

$Y\to Y0\mid Y1\mid 0$

From $X\to 0X\mid 1X\mid 0$, $X$ generates any binary string ending with $0$.

So, $X=(0+1)^*0$.

From $Y\to Y0\mid Y1\mid 0$, $Y$ generates any binary string starting with $0$.

So, $Y=0(0+1)^*$.

Now,

$S\to XY$

So, every string generated by $S$ contains one $0$ from the end of $X$ and one $0$ from the start of $Y$.

Therefore, every generated string has at least two $0$'s.