We explicitly describe the KSBA/Hacking compactification of a moduli space of log surfaces of Picard rank 2. The space parametrizes log pairs
(
S
,
D
)
(S, D)
where
S
S
is a degeneration of
P
1
×
P
1
\mathbb {P}^1 \times \mathbb {P}^1
and
D
⊂
S
D \subset S
is a degeneration of a curve of class
(
3
,
3
)
(3,3)
. We prove that the compactified moduli space is a smooth Deligne–Mumford stack with 4 boundary components. We relate it to the moduli space of genus 4 curves; we show that it compactifies the blow-up of the hyperelliptic locus. We also relate it to a compactification of the Hurwitz space of triple coverings of
P
1
\mathbb {P}^1
by genus 4 curves.