I realise this is a bit free, but I think it's what would actually be said in English, and indeed it is frequently said, especially in relation to the Board of Directors of a company:

https://www.google.es/search?num=100&hl=es&q="highest govern...

Of course you can say "management and control", but although "managament and control body" and "management and control authority" are found, it's not actually a very common collocation, and I can't find cases of "highest/supreme managament and control body/authority" or similar: it just doesn't seem to be said like that in practice.

To conflate "gestión y control" into "governing" seems to me legitimate; "governing" involves laying down the law and dictating how things are to be run: exercising administrative authority.

"Highest governing body" could also be said, but I chose "authority" because "governing body" is itself a common term for the highest authority in an organisation, so it sounds a little odd to me with "highest".