Counting rational points on non-uniruled surfaces

Let $X\subseteq \mathbb{P}^n$ be a non-degenerate non-uniruled irreducible projective surface of degree $d$ defined over a number field $K$, and let $N_{X^{\prime}}(B)$ be the number of rational points of $X$ of height at most $B$ that do not lie on lines contained in $X$. Assuming a suitable hypoth