far from; anything but; let alone
どころか (dokoro ka) is used to say that something is far from being the case, often followed by a statement that is the opposite or even more extreme, meaning 'far from' or 'let alone'.
This pattern expresses a strong contrast. It sets up an expectation and then denies it completely, often adding something even more extreme than the opposite. For example, saying something is not just not cold, but actually hot. It also can be used to say 'let alone' when the second clause is more extreme than the first, often in negative contexts (e.g., 'I can't even run, let alone swim'). The nuance is emphatic and often surprises the listener.
Note that どころか also has a different usage meaning 'even so' or 'however', but that is a separate grammar point. Here we focus on the 'far from' meaning. In speech, it is common and not overly formal, though it appears in both spoken and written Japanese. It is a useful pattern for expressing strong disagreement with an assumption.