alright... standard disclaimers apply. i'm not responsible if you _____ (fill in the blank with whatever catashtrophe comes to mind). i would highly recommend that you put together a design, and have it reviewed by a competent structural engineer or architect.
that out of the way, from an engineering standpoint, i believe the load bearing capacity of a 4x4 beam (loaded as a column) is pretty high. if i were designing this for my home, i would use two identical frames for the top and bottom of the stand. the legs would sit on top of the bottom frame, and the top frame would sit on top of the legs. i would NOT mount the legs to the inside of the top or bottom frame.
consideration for bending of the top frame "joists" and buckling of the legs (colum buckling) are the two main concerns here.
check this article about replacing load bearing beams in a porch. at the end of the article, it has some equations for determining adequate beam sizes.
i would use the worst case load bearing capabilities that he listed. i would also shoot for a 2X or 3X safety factor. that means, when you determine the required cross-section for your beam, up it by 2 or 3 times. if these are beyond your understanding, dont design a stand for that much weight.
i havent found a good writeup about column sizing, but the eight 4x4 legs *should* have adequate buckling load capacity. whatever you design, it WILL need some sort of bracing. squares will not provide any resistance to collapse. you will need to either cross brace every square opening or use a layer of OSB or plywood to provide some bracing support. again, this should be done over all the square openings.
PLEASE run your deisgn by a qualified individual. paying someone a few hundred dollars for a certified design will be MUCH less than it would cost you to clean up a 360 gallon mess from your home. i was nervous about my 55 gallon stand design, i cant imagine how i would feel designing a 360 gallon tank stand.