@Linkat,
Homework, or lack thereof, shouldn't be graded in the same manner as tests and the like, and should certainly not weigh in on the final score. By doing so, it will allow people who are smart enough to get high scores for a certain test to neglect their homework and still score a pass. That's not the sort of attitude you want to teach students in school.
Rather, make a separate system: check the homework of three random students each lesson. If they didn't do the homework, give them a strike. If any student goes up to three strikes during the semester/trimester, they are out. Out as in, an automatic fail for the course.
As a teacher, you could demand all students hand in their homework assignment a couple of times, just to make sure no one plays the odds (if they have no strikes, just neglect homework until they have two or some such).
Now, if someone fails a course due to not making their homework, even if they get an A for the tests and exams overall, it'll show up on their final results. I think it's relevant for a college to know if a student has not just the brains to excel in a given course(as reflected by their grade), but is also willing to put in the work to master the course(as reflected by the homework pass or fail).
Just my idea.