If the company deals only in permissible shares, then there is nothing wrong with working on a program that enables clients to buy and sell these shares via the stock exchange. But if it deals in both haraam and permissible shares, it is not permissible to help with that, by programming or otherwise, because it comes under the heading of cooperating in sin and transgression, and Allaah says (interpretation of the meaning):
“Help you one another in Al‑Birr and At‑Taqwa (virtue, righteousness and piety); but do not help one another in sin and transgression. And fear Allaah. Verily, Allaah is Severe in punishment”
Sin is not limited to the one who deals directly with the haraam thing, rather it also affects the one who helps him with that, approves of it or promotes it.
Based on this, if you are certain that the company only deals in permissible shares, then there is nothing wrong with you accepting a job with them.
We ask Allaah to guide you.
And Allaah knows best.