My patent application describes software method. I wrote the code just to test it. It is stripped down embodiment, as real things would be more complex and depending on particular implementation. All software patents I read don't have code attached. I am reluctant to submit my code as it is not simple and require a lot of explaining.
In a computer related invention, the patent application may disclose a computer processor or other hardware that may be sufficient for enabling a general computing function. However, mentioning a computer processor or hardware may not be sufficient for enabling a structure for performing a specific function, since novelty in computer related inventions most often resides in the software or the computer program that is being executed on the computer processor and not the hardware itself.
When it comes to identifying the “corresponding structure” for a computer related invention, an “algorithm or code” is the one which carries out the claimed function, and therefore the specification must disclose the "algorithm" that can be used to perform the claimed function.
The algorithm however, need not necessarily be in the form of source code; the algorithm may be expressed in any understandable terms, such as mathematical formula, in prose, or as a flow chart, or in any other manner that provides sufficient structure.
You may visit the link http://www.invntree.com/blogs/disclosure-requirements-for-software-patents for further details on disclosure requirements of software patents.
I am reluctant to submit my code as it is not simple and require a lot of explaining.
That's a good reason to submit code.
Your patent (and consequently application) should give other people the ability to practice your invention.
So no, you do not need to include code, and as you said, many people do not, but you should (almost definitely, and "almost" is a technicality) include some form of code. It doesn't have to be compilable, but you should have some flow chart, pseudo-code, or, yes, actual source code.
This isn't an actual standard or anything, but in general I would set your goal as that for anyone who's read your application, your code shouldn't require a lot of explanation.
Think ultimately of how you would explain the invention to a fellow developer. Would you include source code, or just drawings on a white board?