If you want 4096 bytes of memory as a minimum, and you’re somehow storing the data in some kind of cheap (or even homogeneous) passive elements activated by intersections of wires, and you want to minimize the number of wires, you need ⌈√(4096*8)⌉ = 182 wires in each direction, a total of 364 wires. If you do it in the more usual way, you need 128 wires in one direction and 256 in the other, for a total of 384 wires.
Ferrite cores are the most typical way of storing data in such a memory, but there are other possibilities as well, even at the ferrite-core macroscale. For example, you could imagine a ferroelectric material sandwiched between two layers of indium tin oxide electrodes, one vertical and one horizontal, like an LCD but with PZT or whatever replacing the liquid crystals; or an e-ink (electrochromic) display.