  We show that up to automorphisms of $\mathbb{P}^2_{\mathbb C}$ there are $5$
homogeneous convex foliations of degree four on $\mathbb{P}^2_{\mathbb C}.$
Using this result, we give a partial answer to a question posed in $2013$ by D.
{Mar\'in} and J. {Pereira} about the classification of reduced convex
foliations on~$\mathbb{P}^2_{\mathbb C}.$
