Is there a word for a personal or informal definition?

In a general context, the word definition does not necessarily imply a dictionary definition. So, your use of "my definition of good C# code is ..." is perfectly fine. If you want to stress that it's your personal viewpoint, you would employ the word opinion as follows:

In my [personal|considered] opinion, good C# code is defined by ...

For an informal definition, you could use:

A loose definition of ...

Or, if you are simplifying a definition in the interest of your audience:

A layman's definition of ...

First, you say "If we're speaking English, the definition of a word should be its corresponding text in the dictionary." but that's not really true.

There is no 'official' English dictionary since there's no 'official' definition of the English language. The English language is defined by the community that speak it and evolves over time. Dictionary-makers are just well-meaning people with expertise in lexicography who do their best to give us useful tools that reflect usage. Dictionaries are helpful, and the respectable ones carry a lot of authority - but that authority is due to the painstaking research and work that went into them, not just the virtue of being called a 'dictionary'.

Each of us is free to make our own definitions that fit the context we're dealing with. "Definitions" are just explanations of a word's meaning using some paraphrase. What really matters is communication and being understood.

That all said - if you say "the definition of good C++ code", the use of the definite article means you are referring to a particular definition. It may be Webster's or Stroustrup's. If you say "my definition of good C++ code", then it's clear that you are referring to a personal definition which may not be found in a published book.