This is a little informal to me and strongly suggest you write a targeted cover letter for each one you send out using an existing job description or at least targeted role at a specific company.
A cover letter I would love to see:
"Hi,
I was excited to see your job posting for an entry-level bioinformatics software developer and would like the opportunity to speak with you further about the role.
Specifically, I see you are seeking a developer with experience with Linux, SQL, shell scripting, and some Ruby or Clojure programming experience. My primary development environment is Linux - I used to use Arch, but have shifted to Ubuntu for simplicity's sake.
My Ruby/Clojure experience is limited, but here is a link to a project I did as a learning experience on github (<insert link here>). The project was created to do (<insert short description here>) and originally used Ruby, Sinatra, and a PostgreSQL backend. I have recently started porting it over to Clojure/Compojure.
I have attached my resume, which contains some short descriptions of work I did as an (intern/student/previous job) that demonstrate the background you are looking for.
Thanks for considering me as a candidate,
<me>
ps - if we meet and decide to go further in the process, I am happy to provide references at that time."
Even the above is a little informal - you might want something a little more conservative for a big company. I think of the above as having a conversational tone, which is personally comfortable for me.
But, if you send me the above letter and I think your code examples don't look like a complete travesty, I am at least going to interview you.
There isn't a lot of information actually in the example text, but to be honest (and keep this mind) - I want you to be the one. I am going to read between the lines of the cover letter, generally assuming the best. If I got the above, I am going to think, ok, here is a candidate who bothered to write me a cover letter, addressed my job requirements, and looks like they at least have some initiative.
Anecdotally, I have friends who run small consultancies that have literally received one-liner responses to job posting: "I can do this and my rate is $95 an hour"
Anything you do better than that probably helps your case.
Also, it is an old horse, but I'll beat it again - try to weasel a real contact in your network to make a recommendation or introduction. I am not particularly good at that personally, but it makes a huge difference when it happens.