This is corrected (silly me, sorry):
Assuming my calculations are correct (it gets tricky!!!), the first few elements of $T$ would be:
$$T = 1,2,3,0,4,\omega,5,6, \omega + 1, \omega +2,7,8, \omega + 3,\omega+4,\omega \cdot 2,9,10,\omega+5,\omega+6, \omega \cdot 2 + 1, \omega \cdot 2 + 2, \dots$$
The first iteration would generate $0$ based on Rule 1 and $(3,2,1)$. It would also generate $4$ and $\omega$ based on Rule 4 and $(1,2,3)$. These are then added to $T$ to complete the first iteration.