The following answer is just my opinion and might not address your particular situation. To oversimplify a bit, most students either
want to do the homework for their own reasons (enlightenment, fun, or preparation for the exams,) or
only do the homework in order to receive credit.
To get group (1) to take the homework seriously, you don't need to do anything at all. So let's just consider group (2).
If you want them to take it seriously, then you need to grade it carefully and only give credit for work that demonstrates understanding. If you grade based on "completion" then they will (rightly) understand this to mean that a nonsense answer is as good as a correct answer. A nonsense answer is easier to write, so the choice will be clear to them. Also, they will think "if the instructor can't be bothered to grade properly, then why should I bother to write a proper answer?"
So if you want more students to take the homework seriously, but you don't want to grade more carefully, you will need to make more students from group (2) move over to group (1). The straightforward way to do this would be to make the homework more enlightening, more fun, or more relevant to the exams. You can make sure the homework is relevant to the exams when you write the exams, so let's think about how to make it more enlightening and fun.
This is a hard problem in general, but one easy thing you can do is to simply give fewer problems that are less tedious. This makes it feasible for more of the students to turn in their own work, rather than giving up and writing nonsense or copying the answers from another source. It is hard enough for a student to understand one new concept per week, so the instructor should focus on making that happen rather than assigning dozens of exercises with the unrealistic expectation that the student will understand them all simply by virtue of being forced by the grading scheme to "do the work."
To summarize, a simple way to get the students to take the homework more seriously may be, paradoxically, to make it easier. (The downside is that you will have to select the problems more carefully and make sure the students understand that they need to understand all of the problems in order to be prepared for the exam.)