You are using an HDMI to Single-Link DVI adapter. HDMI to Dual-Link DVI adapters do not exist as HDMI does not support that capability, any adapters you find labelled as such are fake. The only way to connect to your monitor is through a native Dual-Link DVI port (unlikely on a laptop) or a $100 DisplayPort to Dual-Link DVI converter.
See here:
https://linustechtips.com/main/topic/729232-guide-to-display-cables-adapters-v2/?section=high_refresh_displays
In regards to HDMI 1.4, it is capable of 1080p 144 Hz, but many monitors choose not to implement that capability, including the Acer GN246HL that the OP is using (though there
are examples of monitors that do support 144 Hz over HDMI 1.4, and in fact I own one).
See here:
https://linustechtips.com/main/topic/729232-guide-to-display-cables-adapters-v2/?section=hdmi_60hz_limit
This capability of HDMI is irrelevant anyway though, since the OP is using an adapter. Compared to a Single-Link DVI/HDMI 1.2 connection which both use a single TMDS link at 165 MHz (≈1080p 60 Hz) HDMI 1.4 supports 1080p 144 Hz by doubling the signal frequency from 165 MHz to 340 MHz, but still single-link. Dual-Link DVI supports 1080p 144 Hz by adding a second TMDS link, while the signal frequency is kept at 165 MHz.
When using a passive HDMI to DVI adapter, you will not have a second TMDS link because the HDMI connector only has pins for one link, and you will not have the increased signal frequency because the DVI port on the receiving end will (probably) not support more than 165 MHz. So you are limited to a Single 165 MHz link, which means no more than 1080p 60 Hz. Yes, HDMI and Dual-Link DVI both support 1080p 144 Hz, but they support it via different methods, and neither of them supports the other's method of doing it.
(Though I should mention there are some exceptions, as some displays have DVI input ports are capable of running at up to 340 MHz even though this is outside DVI spec, but in these cases HDMI to DVI passive adapters will work for full HDMI 1.4 bandwidth, for example the Dell U2711, which can reach 2560×1440 through an HDMI to DVI adapter; but this is very rare).