Do similar adaptations result in similiar genetic code?
It can be the case but it is not necessarily the case. You sure can have the same mutation happening and raising in frequency in two independent lineages but you may well also have different mutations leading to similar adaptations in different lineages.
Example
As you talk about humans, let's take an example from humans. The ability to digest lactose (milk) at adult age has evolve several times independently. I just copy-pasted from this answer of mine
Gene LCT
Mammals have a gene (called LCT C/T-13910) coding for the lactase enzyme, a protein able to digest lactose. Lactose is a disaccharide sugar found in milk.
Expression of LCT
In mammals, the gene LCT is normally expressed (see gene expression) only early in development, when the baby feeds on his/her mother's milk. Some human lineages have evolved the ability to express LCT all life long, allowing them to drink milk and digest lactose at any age.
Today, the inability to digest lactose at all ages in humans is called lactose intolerance.
Three independent mutations
Tishkoff et al. 2007 found that the ability to express LCT at an old age has evolved at least three times independently. Indeed, they found three different [SNPs][6] (stands for Single Nucleotide Polymorphism; it is a common type of mutation), two of them having high prevalence in Africa (and people of African descent) and one having high prevalence in Europe (and people of European descent). The three SNPs are G/C-14010, T/G-13915 and C/G-13907.
In this example we can know that the ability to digest lactose at adult age evolved at least 3 times independently. It is quite hard to tell whether it had evolved more than three times. It is indeed possible that the mutation G/C-14010 had occurred in two independent lineage but it would be hard to disentangle them today if the two lineages are not clearly geographically isolated (and in humans, very few populations are really isolated from the others).
