My suggestion is: don't try to fix it. As an engineering manager with a team of more than 5 people, coding is no longer the most impactful thing you're doing. Making people and the team do better is far more leverage. As a fellow EM who also loves code, I've stopped coding at work. I find there are many, lot more impactful activities I can do: from hiring activities, onboarding & training, making oncall better, spending more time with my high & low performers and building bridges with fellow EMs, PMs, executives and other stakeholders and so on.
Also, you've not mentioned 1:1s. With a team of 12, 1:1s take a lot of my time (I do weekly 30mins - this is a lot, but has been essential to spot issues early and support people better)
Good luck for 2018!