It might be impossible... And if not impossible then you might have to travel a long way to get around any gaps.
I remember when I was still in my starter sidewinder, I wanted to get to the high tech system GD219. However it was 15Ly away, which was beyond the range I could jump, and there were no systems inbetween. I did manage to plot a route to it, but it would have been 16 jumps.
If you can afford it I would buy as much stuff as possible to help you jump further. Sell your weapons, even your shields if you feel brave and can evade interdictions. Keep your BDS if you like, you might be able to make a little money along the way. Upgrade mandatory modules to D, which are lightest and help you jump further.
You can sell all this stuff when you get to Leesti for the same price you paid for it and re-equip your sidewinder how you want it. It will cost you some money though because all the equipment on the Sidewinder is loaned to begin with, so you get no money for selling it, but if you want to buy similar equipment in Leesti then you wil have to pay for it.
When plotting the route you have to give the Galaxy map time to work out all possible routes, and this can take a long time. Only once the expanding sphere of possible routes (grey lines) reaches Leesti can you plot the course there. If the sphere starts to reach systems 100Ly away but not Leesti then you know you can't get there, unless Leesti is more than 100Ly away as the map won't plot routes that far away. You'll have to jump to the edge of the sphere closest to Leesti first and then plot again.
Cargo adds to your weight so either don't carry any, or buy the cargo before plotting the route so that it takes into account the extra weight. There is a slider allowing you to plot a route with x tons in the cargo hold before you actually buy the cargo but it's been known to be inaccurate. Fuel also adds to your weight so if you wanted to be really clever you could refuel little and often, never keeping more than about a third in the tank, but this is risky and the time it saves in longer jumps might be lost again in frequent fuel stops. The Galaxy map route will turn from a solid to a dashed line at the point it predicts you will run out of fuel, but keep your eye on the fuel guage, the blue part shows what will be used in the next jump. If you're going to use more than half of your fuel to make the jump and you know that the next system has nowhere to refuel or you aren't sure then the time to refuel is now. Be very careful because as well as using fuel in the jump, it frequently also tops up the reservoir used to run your ship's systems, so it can look like you have enough fuel to jump and then jump back if there's nowhere to refuel but then the reservoir refills and you suddenly can't get back to where you came from.