Is there a way to complete a sudoku where you have to make sure all even digits are orthogonally connected to all the others, while avoiding 2x2 squares of even digits?

It is known to be possible when 2x2 squares *are* permitted - see, for example, the following arrangement:

[![with squares][1]][1]

But is it possible while avoiding 2x2 squares of even digits?

 [1]: https://i.sstatic.net/ngpRi.png