Well we can infer that honor killing is Haram according to the Quran if the fornicator was a virgin at the time of fornication. Their punishment is 80 lashes, and optionally disowning.
The conditions for applying the "Had" punishment, which is killing, are:
1-The fornicator must be a non-virgin
2-There must be 4 eye witnesses
3-They must witness the penis penetrating the vagina. Even if 4 people saw a woman and a man lying in the same bed, that is not enough to apply the punishment.
Of course, if all conditions are met the punishment is stoning to death