Keyboard – Multimedia key mistaken for an ASCII character

My new laptop has a set of multimedia keys that control brightness, volume, play / pause, and more.

Most of them work with Ubuntu 18.10 (+ i3wm), with the exception of one. On F4 is a touch "mode of presentation", which I hoped to link to something useful. Strangely, pressing this key prints only the lowercase letter "p".

Effectively, xev returns very similar results for both keys:

The multimedia key returns

KeyPress Event, Series 28, Synthetic NO, Window 0x2400001,
root 0x167, subw 0x0, time 42090837, (682,799), root: (1645,825),
state 0x40, keycode 33 (keysym 0x70, p), same_screen YES,
XLookupString gives 1 byte: (70) "p"
XmbLookupString gives 1 byte: (70) "p"
XFilterEvent returns: False

KeyRelease Event, Series 28, Synthetic NO, Window 0x2400001,
root 0x167, subw 0x0, time 42090905, (682,799), root: (1645,825),
state 0x40, keycode 33 (keysym 0x70, p), same_screen YES,
XLookupString gives 1 byte: (70) "p"
XFilterEvent returns: False

while p results

KeyPress Event, Series 28, Synthetic NO, Window 0x2400001,
root 0x167, subw 0x0, time 42207819, (-91,844), root: (872,870),
state 0x0, keycode 33 (keysym 0x70, p), same_screen YES,
XLookupString gives 1 byte: (70) "p"
XmbLookupString gives 1 byte: (70) "p"
XFilterEvent returns: False

KeyRelease Event, Series 28, Synthetic NO, Window 0x2400001,
root 0x167, subw 0x0, time 42207867, (-91,844), root: (872,870),
state 0x0, keycode 33 (keysym 0x70, p), same_screen YES,
XLookupString gives 1 byte: (70) "p"
XFilterEvent returns: False

Meanwhile, the other multimedia keys return a completely different output format, for example:

KeymapNotify Event, Series 28, Synthetic NO, Window 0x0,
keys: 4294967184 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

xmodmap, of course, gives the keycode 33 as

key code 33 = p p p thorn THORN thorn

How can I make sure that both keys are recognized as distinct?