A portion only refers to a part, piece, section, chunk, segment, slice or fragment, so it's highly unlikely it is referring to any wholesale decryption. Significant does not mean large part, only notable, remarkable, consequential or conspicuous, so the claimed 'solution' could be just a small feature of the 340 cipher, dressed up in wording to imply a greater find.
There are some notable features present on the 340 cipher, and here are three.
The first was presented in an article by Jos Kirps, which is not readily available on the internet anymore with a cursory search. It involves the blending of the 'Halloween' card and 340 cipher, in which the wording Paradice and Slaves from the 'Halloween' card forms a cross formation within the 340 cipher, with corresponding characters (see below)
In this image I have placed the additional phrases By Fire, By Gun, By Rope and By Knife from the 'Halloween' card in the respective quadrants of the 340 cipher
The second interesting feature is the corrected sixth line of the 340 cipher. In 2012 I found a tenuous link from this portion of the 340 cipher to the 'Exorcist' letter mailed four years later. See here.
The third notable area of interest is the 'near Zodiac' placed on the 20th line of the 340 cipher, almost signature like. Was this a random array of characters, or was it specifically designed by the author and killer for a reason. I have suggested a possibility for its design, linking the '13 Symbol' cipher and 340 cipher as a form of continuation. See here.
These three offerings may have nothing to do with the History Channel revelation next Tuesday, and none were maybe what the Zodiac Killer intended, but I would like your opinion and suggestions to the claim "the team says it may have solved a significant portion of the diabolically complicated Zodiac code, Z340." What do you believe they have found.
Fox News article: