I am assuming that the intelligence we are talking about is the type that leads to 11 A*s at GCSE and a first class honours degree from Oxford university? If that is the case, then this type of intelligence is not due to the presence or absence of a particular gene. Rather, it is due to the presence (or absence) of several genes, and the conditions in which the individual is raised.
Intelligence is not a black and white trait. People in general are not either intelligent or unintelligent. Instead, there is a scale, ranging from the brightest person in the world to the dimmest. Everyone is on the scale somewhere. However, your position is likely to change according to the intelligence' that is being considered. Perhaps you're a genius at maths but rubbish at English, does that make you intelligent or not?
We all inherit half of our genes from our dads and the other half from our mums, so our DNA is a mixture of the two. Remember though, that they also inherited half of their genes from each of their parents and so on through the generations. This can result in many gene variations, only some of which we will inherit. The particular variations we inherit are completely due to chance. That's how people can be closely related (brothers and sisters etc ) but look completely different or have polar opposite personalities. It is possible to inherit genes that can give you certain advantages in learning, such as a better natural memory skills, but there is no such thing as a 'fantastic at french' gene.
Certain personality traits and the ways in which people are raised can also play a role in intelligence. Possessing genes that give a naturally higher intelligence is fine, but if someone is more interested in having fun than learning, or are not encouraged to study, they're unlikely to do as well in exams as someone with lower natural intelligence, who works hard. It could be argued that characteristics such as stubbornness or perseverance contribute as much to intelligence as a better ability to learn. We know that possessing genes for certain traits does not always mean that they contribute to who we are. If genes were the be all and end all, then identical twins would be like two copies of the same person, when in fact they are not.
Basically, there is no such thing as a gene for intelligence. There are many genes and many variations of genes in the human genome. Possessing certain variations of certain genes may assist in learning particular skills, but they by no means guarantee intelligence. It is also worth considering other types of intelligence, such as emotional or social intelligence, which could be valued just as highly as the ability to multiply large numbers in your head.