  The ring in the title is the first non commutative ring to have been used as
alphabet for block codes. The original motivation was the construction of some
quaternionic modular lattices from codes. The new application is the
construction of space time codes obtained by concatenation from the Golden
code. In this article, we derive structure theorems for cyclic codes over that
ring, and use them to characterize the lengths where self dual cyclic codes
exist. These codes in turn give rise to formally self dual quaternary codes.
