Can the high efficiency washing machine drain into the kitchen waste stack?
Firstly, disclaimers: I have no idea what rules might apply in the US, and I have also never heard of a "high efficiency" washing machine. I shall therefore answer from the point of view of practicality, and the assumption that "high efficiency" doesn't affect the water coming out of the washing machine's drain hose.

Size of particles: waste water from your washing machine presumably goes through a relatively small diameter hose. It therefore isn't going to have any problem going through your kitchen drainage stack (which should handle small pieces of food waste).

Type of water: waste water from your washing machine is going to have detergent in it. Just like water from your kitchen sink. I can't see any reason why the stacks would connect to different sewers, and therefore I can't see any reason why a national (US) or local (Boston) code would prohibit washing machine waste water from entering the same stack as kitchen waste water.

My experience: in the UK it is normal for a house to only have one drainage stack, which the bath water, toilet flush, kitchen sink and washing machine all discharge into.

In summary: I would find it very unlikely that you wouldn't be able/allowed to drain your washing machine into the kitchen stack.