Highest dimension commutative ideals of a niltriangular subalgebra of a Chevalley algebra over a field

Let $N$ be a niltriangular subalgebra of a Chevalley algebra. We study the problem of describing commutative ideals of $N$ of the highest dimension over an arbitrary field. It is proved that $N$ contains a commutative ideal of this dimension, and all such ideals are found. In addition, all maximal commutative ideals of $N$ are described for the types $G_2$ and $F_4$. As a consequence, the highest dimension of commutative subalgebras in all subalgebras of $N$ is found.