Regex for bit strings with at least two zeros but no consecutive zeros This is what I have:

$$(1^*011^*011^*)^*\,.$$

But I don't think this is accounting for an odd number of zeros, like "$10101010101111$". I think I have the right expression that satisfies no 2 consecutive zeros and even number of zeros. Can someone help? Thanks!
The shortest regex I came up with is: 1*01+0(1+0?)*


Start with arbitrary amount of 1s (1*)
Exactly one 0 (0)
One or more 1s (1+)
Another 0: (0)
Arbitrarily often ((...)*):


One or more 1s (1+)
At most one 0 (0?)