Minimize the longest King chain on a 7x7 binary grid

This puzzle is an extension of this one: Minimize the longest King chain on a 5×5 binary board

Given a grid filled with numbers, we define a King chain to be a path on the grid such that:

1. The path can be traversed with chess King’s moves (moving to one of 8 adjacent cells at a time),
2. The numbers on the path are all equal, and
3. The path does not visit any cell more than once.

The length of a King chain is the number of cells visited by the King.

Can you find a 7×7 grid filled with zeros and ones, such that every pair of zeros and every pair of ones are connected via some King chain, and the longest King chain is as small as possible?