It doesn't exist.
There used to be a bug with Vulcan Minigun that made you run faster with short barrel mod, but it's been patched long time ago. Like 5 years ago with update 83.
not sure what you mean with gun that increases speed, it could be the minigun glitch mentioned above, but you maybe mean the judge shotguns with HE rounds to lower your health and break your armor to get the yakuza boosts and second wind boosts
sliskiepalce is still here. QQ you did great runs some years ago - i watched them all, some time ago! and i was thinking on this minigun bug too that gives you 20% more speed (if i remember right) by equip 2 mods back then.
Hey runners! A bit late of an announcement of the new categories voting results, but they all ended up being voted in favour of, so we decided to announce it when the new categories along with the rules, as well as the new version of the speedrunning mod that includes the "no slowmotion" toggle are
