I am taking another home.

I chanced to listen to a song, 'Morning train' by Sheena Easton.
It was so good and sweet.

Of the lyrics, I had some which were hard to figure out.

My baby takes the morning train.
He works from nine till five and then,
he takes another home again.

The third line, 'take home' is rather unclear to me.

My guess from the context is that
he takes another train which goes to my place again.

Is it okay to say 'take home'
as a way of saying 'take a train bound for my place'?

I mean, if I said 'I'm taking home' when asked where I was going,
would it be good enough, causing no confusion or he or she might want further information to see what I exactly intended to say?

Any comments would be appreciated.
Thank you.