At companies 99% of the time it is former or current coders who hire other coders.
And coders don't care about how old you are. It is all about what you have done and what you can do. So the best thing you can do to get yourself noticed is to build and show something great. It doesn't have to be huge just needs to work, be bug free and polished.
I think that would be a first in the annals of the industry :) I assume you really mean 'no obvious/glaring bugs'. Of course that could also be satisfied by Hoare's famouse quote [1], or by simply being so trivial as to not allow the oppurtunity for a bug.
[1] There are two ways of constructing a software design. One way is to make it so simple that there are obviously no deficiencies. And the other way is to make it so complicated that there are no obvious deficiencies.
And coders don't care about how old you are. It is all about what you have done and what you can do. So the best thing you can do to get yourself noticed is to build and show something great. It doesn't have to be huge just needs to work, be bug free and polished.