I think they should invest heavily in artificial womb technology, the production of new life and citizens should be centralized at state level, you can't leave that huge responsibility to individuals, nobody should have the right to breed freely.
Once new human life can be effectively and safely spawned in a lab, you can release a neutering agent in the water supply so that all human females will become infertile, then you can produce babies in artificial wombs and after birth, educate them in govenment facilities and institutions, creating a new generation of perfect citizens.
This way you can enforce strict eugenics criteria, you can also ensure the indoctrination of the child with society's core values.