If you have developed the Software and will continue to render support services to that software you also have access to the Data, therefore you act as a Processor (it's not a matter of you deciding or not to access it, it's a matter of having the possibility to access the Data).
If you have developed the Software and will never again "interact" with it, then you are not a Processor nor Controller.
Now speaking of Controller, if the software was developed under Client instructions, the Client is the Controller, however if you have a software suite that enables by default some features and the Client may chose some or all + you maintain the tool (support services), then you are in fact a Co-Controller (not just a Processor).
You really should do your own internal operational assessment, unless this is the only client you have.
Opposite to what Amon just said, Processor Status does not require a Contract with the Controller... you can be a Processor with no Contract whatsoever, be very careful with that... now this means that you should (must) have a contract so that both parties are "protected"... if there is no contract both companies are breaching GDPR (if GDPR is applicable of course).
Be very careful with the remark ".. without such contract you are not a Data Processor..." it's not a matter of contract... it's about WHAT you effectively DO!