Any electricians available? Wire size question...

4AWG is rated for 105 amps on a se cable so you should be just fine with that in the distance you are running. To meed National electric code it needs to be buried a minimum of 24" below grade. I have alway thrown a 2x4 over the top of direct burial cable so it atleast gives someone a clue there may be something going on if they are digging and hit it.