An algebraic foliation of $\mathbb{C}^2$ which admits a non-algebraic complex limit cycle $L$ with $L\cap \mathbb{R}^2=\emptyset$

Question

Is there a polynomial vector field on $\mathbb{R}^2$ whose corresponding singular complex foliation of $\mathbb{C}^2 $ admits a complex limit cycle $L$ such that $L$ does not intersect the real plane $\mathbb{R}^2 $, moreover $L$ is not an algebraic leaf?

The following paper provide an example of this situation except the non-algebraic requirement.

In Question 1 of this note we pose the above question

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