Let $X$ be a smooth plane projective curve of degree $6$ and genus $10$ (over complex numbers). Then my question is the following :

**Question :** Is it possible that there exists a special divisor $D$ of degree $9$ on $X$ admitting exactly $4$ independent sections?

**Observations :** $(i)$ From Clifford's theorem: we have, $h^0(\mathcal O_X(D)) -1 =3\leq \frac{\text{deg}(D)}{2} =4.5$. Therefore, this theorem says that such divisor may exists on $X$.

$(ii)$ Note that, if such a divisor exists on $X$, then it belongs to $G^3_9(X)$. Since, $\rho(10,3,9)=-6<0$, we can't guarantee the non-emptiness of $G^3_9(X)$.

Any insight or remark from anyone is welcome.