  In this paper, we study holomorphic foliations of degree four on complex
projective space $\mathbb{P}^n$, where $n\geq 3$, with a special focus on
obtaining a structural theorem for these foliations. Furthermore, for a
foliation $\mathcal{F}$ of degree $d\geq 4$ with a sufficiently high
$k^{th}$-jet, we prove that either $\mathcal{F}$ is transversely affine outside
a compact hypersurface, or $\mathcal{F}$ is transversely projective outside a
compact hypersurface, or $\mathcal{F}$ is the pull-back of a foliation on
$\mathcal{F}^2$ by a rational map.
