Any definable type over a model has a minimal set of parameters over which the type is definable.  For technical reasons, this minimal set of parameters is called the "code" of the definable type.  In general, the code of a definable type will be a tuple of "imaginary" elements, that is, elements of Shelah's $M^{eq}$, rather than "real" elements from the original model $M$.  In $p$-adically closed fields ($p$CF) like the field of $p$-adic numbers, we show that the codes of definable types are always tuples of "real" elements.  This can be used to show that the quotient of a definable set by a definable group $G$ is definable (rather than interpretable) when $G$ satisfies the technical condition "definable f-generics" (dfg).  This explains previous phenomena around dfg groups observed by Pillay and Yao.  In the process of analyzing definable types in $p$CF, we learn some other technical facts about definable types.  These technical facts have applications to the study of definable and interpretable topological spaces in $p$CF.  For example, we show that most notions of "definable compactness" are equivalent to each other, in this setting.  This is joint work with Pablo Andújar Guerrero.