You very likely do not have the right to distribute the code.
The GNU Project's GPL FAQ has this to say on the topic:
Is making and using multiple copies within one organization or company “distribution”?
No, in that case the organization is just making the copies for itself. As a consequence, a company or other organization can develop a modified version and install that version through its own facilities, without giving the staff permission to release that modified version to outsiders.
However, when the organization transfers copies to other organizations or individuals, that is distribution. In particular, providing copies to contractors for use off-site is distribution.
If someone steals a CD containing a version of a GPL-covered program, does the GPL give him the right to redistribute that version?
...If the version in question is unpublished and considered by a company to be its trade secret, then publishing it may be a violation of trade secret law, depending on other circumstances. The GPL does not change that. If the company tried to release its version and still treat it as a trade secret, that would violate the GPL, but if the company hasn't released this version, no such violation has occurred.
Assuming you are an employee, you have received the code as an agent of the company and not as an individual. Thus, the company has not yet participated in an act of distribution (as the GPL defines "distribution"), so the rights of the GPL have not been granted to you personally. You only receive rights under the GPL when you are the recipient of a distribution.
If you really want to distribute this code, talk to your manager or company's legal department to ask for some kind of approval to release the code. Expect the answer to be a resounding "no" unless you have a compelling business argument for why the code should be released.
Addendum: what about after the company starts distributing the code to clients?
Once your company distributes the software to any clients outside of itself, it would seem the nothing has really changed for you. As long as you are not one of the clients that participates in a GPL software distribution, you continue to have the same access you did before (i.e., still an agent of the company, not a recipient of a distribution), and it would appear that the same rules apply.
The only thing that seems to change once any distribution has occurred is detailed in this GPL FAQ entry:
If someone steals a CD containing a version of a GPL-covered program, does the GPL give him the right to redistribute that version?
If the version has been released elsewhere, then the thief probably does have the right to make copies and redistribute them under the GPL, but if he is imprisoned for stealing the CD he may have to wait until his release before doing so.
Several issues here:
In the best case, sharing the code would still violate your employee contract, even if your actions are permissible under the GPL, acting in the role the thief from the above example. You've entered into a contract not to share your company's code, regardless of whether you have a legal right to do so otherwise. You will get fired and may face legal action.
This particular FAQ entry might assume "has been released elsewhere" to mean the software is generally available. However, if your company only distributes its code to a few trusted associate companies, who have no interest in sharing their copies, then a different conclusion may apply.
Even in this example, I'm not sure by what legal mechanism the thief is granted GPL rights. The victim never willingly participated in a distribution, and some comments below note that this situation means that neither the thief nor any of his recipients have grounds to sue if their GPL rights are violated, e.g., they don't get a corresponding copy of the source. Whatever legal mechanism is at play here (assuming this FAQ entry is correct -- I've never seen any case law to confirm or deny it) may not apply to you as an employee who already has access to the code.
I'm not a lawyer, this is hardly legal advice. If you're seriously interested in the answers here, talk to a lawyer.