I find this to be a gray area, with some truth in what everybody is saying.
My feeling is that this "realis/zation" is a mistake here, and implementation is correct.
As someone who thinks more like a descriptive than a prescriptive observer of my native language, the problem is of course that it doesn't matter what the "correct" use is or what I think--if a sufficient number of people start using "realisation" for this then it becomes de facto correct.
The fact that I denounce "I feel nauseous" as incorrect (should be "I feel nauseated"--rotting food is "nauseous") is completely irrelevant since now the majority of my countrymen use it that way--incorrectly, to my way of thinking; but numbers win the day, so soon "nauseous" will be correct. Actually, I have already lost that one--nauseous is "correct" now.
I feel that "realization" in this sense is now in the gray area. I say that it is wrong, you may or may not agree. But in some sense, as a non-native speaker one might want to weigh in on the conservative side of this argument, and thus stick to "implementation", until the native speakers seem to have swayed one way or the other.
On the other hand, if you want to be in the vanguard, or if you were one of the early group of those who said that "es macht kein Sinne" was ok in German (which is perfectly defensible now by the sheer number of those who use it, though I don't like it) then by all means use "realisation".
Another example: when I was in France, some of my American friends spoke (in English) of the amount of the "caution" on their apartment--what they meant of course, was the amount of the "security deposit", which I hastened to point out, as someone who hates Franglish.
In fact, "design and realisation" sounds to me very much like something a bilingual French-English person might use, especially one was so good in both languages they weren't quite sure anymore sometimes of whether these were really "faux amis" or not.
So there--I've had my say about the gray area, so "realize" that there are two sides to this one, figure out whether you're feeling in a funky and avant-garde kind of mood or in a more conservative one, and then take your choice!
By the way, in France whenb we used to say "realisation d'un logiciel" for a software project some of the group would try to translate into the same word in English--always drove me crazy--this clearly must be "implementation" in this context, as nothing "real" comes out of it.
Maybe the anglophone architects feel differently about this, as a building is actually created--realized--but I would never use it this way either. Perhaps an architect friend would care to weigh in on this question.