  In this paper, we describe an algorithm for computing algebraic modular forms
on compact inner forms of $\mathrm{GSp}_4$ over totally real number fields. By
analogues of the Jacquet-Langlands correspondence for $\mathrm{GL}_2$, this
algorithm in fact computes Hecke eigensystems of Hilbert-Siegel modular forms
of genus 2. We give some examples of such eigensystems over $\Q(\sqrt{2})$.
