Visas, and Japan more generally, doesn't have a lot of black and white answers. While in principle you need an engineering visa to work as a developer, a company could hire a marketer who happens to write code without one. I'm not clear exactly what visa you'd need, but I'm guessing Specialist in Humanities.
To get a visa though, you'll need a company that wants to hire you. The more they want to hire you, the more willing they'll be to adapt to your situation. Even if you fit into the standard visa, you'd still be facing an uphill battle getting a job here, so the barrier to getting a job here is quite high, though not insurmountable.
I'd work on marketing yourself as a developer, as this will help you get a job in Japan or anywhere. I'd try to figure out where you can provide unique value over other developers.
One idea would be to see how you can combine your development skills and marketing background. For instance, someone who can not only come up with good A/B tests to run, but also implement them by themselves, is a lot more valuable than a marketer who can just come up with them, or a developer who can implement them. Another would be to help companies with lead generation through tools you can build. It could be as simple as something like this A/B Significance Test calulator, or something more involved.
Even if you decide you want to focus on something like backend development, and not use your marketing background in your day to day work, I'd use it to sell yourself. Developers tend to be quite bad about demonstrating value to potential employers, so you'll have a leg up on others.
I'd also consider holding off trying to get a job here until you have more experience as a developer. Pivoting your career and moving to Japan might be too challenging to do at once. Even if your local town doesn't have so many opportunities, I'm guessing places like Auckland and Christchurch have a decent market. Even Australia would be easier, as you don't face the same language and visa hurdles. Once you have proven experience, Japanese companies will be much more willing to take a shot on you.