Due to the fact how chest, leg, head and hands are distributed, the absolute minimum to get all pieces is exactly 6 weeks:

Code:
       W1      W2      W3      W4      W5      W6

Head                                           T3

Chest  T4      T4      T4      T4

 Legs  T3      T4      T3      T3
 
Hands                                  T3+4
You can fit the remaining tokens inside this table, but you can't get below 6 weeks