FA for |w| divisible by 3 or number of zeros divisible by 2

Working on a question were I should construct a deterministic finite automaton for the language

$ L=\{w\in \{0,1\}^* \mid |w| \mod 2 =0 \lor |w|_0 \mod 3 =0 \}$

The DFA for the two sublanguages is clear, and also howto construct a nondeterministic automaton from these. However my DFA look horrible complicated. Is there a better one than this:

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