I am more of a SW guy, but I couldn't help but notice that 24 * (2 * 2 * 2) + 24 = 216, the frequency you measured.
Probably a mixing of the third harmonic with the base frequency.
From my limited HW design knowledge I gathered, the source is often the supply lines, less often driven IO lines. Perhaps you need to add some RF filtering. Buffer caps (electrolytic caps) are very bad at this.