Realization of all genus 2 reduction types over the rationals

Let $C$ be a genus $2$ curve defined over $\mathbb{Q}$, and consider the 54 reduction types in the genus $2$ classification.

Realization conjecture. All 54 reduction types of the genus $2$ classification are realised over $\mathbb{Q}$.

The classification currently has 53 of its 54 cases realised by genus $2$ curves over $\mathbb{Q}$ of conductor at most $2^{20}$; the missing case is (D21). The conjecture predicts that a curve of type (D21) exists over $\mathbb{Q}$, presumably with larger conductor.