Looking into a 14.5 build and read a number of posts about how the Colt M4 SOCOM heavy barrel was incredibly accurate.
Is this barrel that heavy SOCOM barrel?
Yes, that is the Colt SOCOM barrel.
I love my Colt 14.5 SOCOM Barrel…
Untitled by Cory Fluck, on Flickr
Untitled by Cory Fluck, on Flickr
Could always get a factory colt barrel with this rifle, they recently released the LE6920 HBPW which comes with this barrel and a pinned and welded brake for about $1000. Just in case ya didn’t see them. 
Is there a 16" version of this, or even an 18" or 20"?
I was not aware of this - great idea and thanks!
No.
C4
Is this medium SOCOM profile & carbine gas system easier to suppress vs the 14.5” midlength barrel?
No. 14.5" middy’s are easier to suppress (less pressure).
C4
Thank you. I don’t mean to Bogart the thread, but I have both barrels, an Odin Adjustable block & uncertainty as to which barrel would benefit most from an adjustable gas block. Thank you for the answer.
Handled one of the 14.5" Socoms at the LGS the other day and the first thing i noticed was how well balanced it felt. I plan on replacing my 16" socom barrel with the 14.5", it just felt right.
Colt offered a 16” version on complete carbines, but never as a stand-alone part to my knowledge.
BCM offers a 16” SOCOM profile.
I have a Colt M4A1 SOCOM II, with the 16” Colt SOCOM barrel. It’s a hammer, way more accurate than I expected a chrome lined barrel to be.
The Trijicon ACOG matches VERY well with this barrel. Good luck on your build and keep us posted.
HT