I am looking for an explicit example (i.e. with an explicit Weierstrass equation given) of an elliptic curve defined over a finite extension of $\mathbb{Q}(i)$ which has good reduction with respect to all non-archimedean valuations (and some argument for why this property holds). Such elliptic curves (up to some caveats which can be ignored here) are the starting point for Mochizuki's IUTT papers.
General methods for obtaining such examples are very welcome, but please accompany such methods with an explicit example.