The increasing geometric sequence $x_{0},x_{1},x_{2},\ldots$ consists entirely of integral powers of $3.$ Given that  
  
$\sum\limits_{n=0}^{7}\log_{3}(x_{n}) = 308$ and $56 \leq \log_{3}\left ( \sum\limits_{n=0}^{7}x_{n}\right ) \leq 57,$  
  
find $\log_{3}(x_{14}).$

Let's think step by step and output the final answer within \boxed{}.
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