I have noticed that whenever I see people approached with comments about the quality of their code (by myself or others) they often say things like "You just don't understand what this code is supposed to be doing."
That is always a red-flag to me. If your code is good the person should be able to tell what the code is doing.
What are this person's specific objections to your code?
There are no absolutes or hard rules and much is subjective and language dependent but as general rules of thumb:
Does your organization have a style guide? Does your code follow it?
Does your code have comments? I like to see at least one comment per functional block of code (function, loop, branch, new level of indent, whatever, depending on language).
Are the lengths of your function limited to no more than a page of text, preferably half a page?
Do your line lengths not exceed 80 columns?
Do you make some effort at making the code visually nice to look at? Is it formatted so like elements line up for easy comparison of lines? I'm a big fan of lining up = and parens etc. to make the code look orderly. It makes it easy to spot differences or errors. It sounds shallow but I also find that when someone has done this it means they care.
Without seeing a sample of your code to tell you if it IS bad there's no way we can advise you. If all you want is a polite way to tell the little twerp to shut up and mind his own business that won't get you fired I'm afraid I don't have much to offer.