There are two Community Goals running, and Tutumu is NOT that far out (although the Colonia CG is 22Kly out!). I believe it to be within 400LY of Starter Space. My 'home' base of operations is around 110LY of Eravate, and Tutumu is 19 jumps away in a fully laden Anaconda (14ly when full, 20 when empty), and 10 jumps back when empty.
It is simple to take part in a Community Goal. First, read the CG details in the Mission Board (you can do this from ANY Mission board) to find out the requirements (be aware that sometimes the CG is after MINED materials, NOT those bought on the Commodities Market (NOT the case here with the Tutumu CG)). If you do not have the Horizons DLC make sure that the stations are not on planets. Then get a load of the required materials, and head to the station specified. Do NOT sell your cargo yet, but go into the Missions Board. There should be mention of a Community Goal here (at this location). Click on the local Community Goal, check it is the one you think it is and have prepared for, and then sign up for it. NOW you can sell your cargo, and it will count towards the CG. You normally will make a profit on the CG runs, but when the CG is completed you will be in line for a reward. You do need to return to the original CG station to claim the reward.
You might want to consider the fact that CG do attract the attention of lots of Players, some of whom may turn up to prevent the CG from completion. Because of this you may well want to go into Private Group or Solo modes. Be careful, and you can earn quite a few credits on CGs. In February I took part in the LHS 3447 Station Build CG, and netted myself over 100Mcr (OK, I was flying an Anaconda with 384T capacity), but I also got 4 new Players in their Sidewinders to join in (as two individual Wings, two Players in each Wing as well as myself). They benefitted from the Trade Dividends earned from being in a Wing with me (every time I sold my cargo (and they were at the station at the same time I was) they got a Trade Dividend worth 5% of my Profit Margin with no effect on myself), and at the end of the CG they each got 1Mcr reward (as well as their profits and the TDs from me). Not long after they all had Cobra MkIIIs!
I would expect the minimum reward (when the CG has completed) to be around 1Mcr, and one run will get you on the bottom reward rung. If you can get into the top 75% you should get over 6Mcr upon completion, based on how far the CG was last night (when I last played).
There was a bug that's been fixed that made the missions tell you the wrong place to look, though, so you could have run into that.
