Possible to get 1440p from a 2012 Mac Mini via mini DP -> HDMI adapter? I recently purchased a 2012 Mac Mini and am attempting to max out my dual monitor setup.

Currently, I connect my Mac to a Dell S2417DG's HDMI 1.4 in via this passive mini DP to HDMI 1.4 cable. According to the specifications, 1440p should be possible, yet macOS only offers a 1080p maximum in System Preferences > Displays.

After some exploration, I found and applied this patch, which made a 2560 x 1440 resolution available in Displays. Enabling this resolution, however, doesn't work, and the monitor indicates that there is no longer an input signal. I have also tried setting up 1440p via SwitchResX and verified that all timings are correct according to the monitor manual, but when I apply the custom resolution, the display stays in 1080p mode.

Is it possible to achieve 1440p via mDP -> HDMI on a 2012 Mac Mini?

I am running High Sierra (10.13.3).

I am aware that a working solution would be to use mDP -> DisplayPort, but my gaming PC takes up the DP slot for 1440p@165hz.
As I suspected and as Allan suggested in the comments, I needed an active adapter. This cable, which is the active version of the passive cable I originally purchased, did the trick; I now have 1440p via mDP -> HDMI.