The Thomas Jefferson Papers includes sheets on which Jefferson appears to be trying to recover the code (THE=19', WE008) used between Robert R. Livingston and John Jay. (This may be termed Morris-Franklin code. See here.)
The first one is labeled "Jefferson to Pinckney, 1794" on the Thomas Jefferson Papers website. This is an excerpt from a letter of 8 August 1782 from Livingston to Jay (see here for the full text in cipher and in clear).
This letter contains many discrete portions written in code. Jefferson transcribed them with the corresponding plain text, the first of which is shown below.
Jefferson copied this portion on lines a.-d. with interlined plaintext but the correspondence between them was lost.
The transcript of the original letter in the Papers of Continental Congress is also interlined with plaintext but does not keep track with the correspondence.
Apparently, Jefferson tried to identify the meaning of each code number by comparing the passages in code with the plaintext. (See here for my similar attempt on Franklin's unidentified cipher, TH=167'.) Jefferson identified "19" with "the" and crossed the word in the plaintext. He further identified "73" with "re". (In both cases, the dot over the code number was omitted in copying.) He further identified "559 80" as "e d", which actually should be read "t ed". This led to another misidentification of "245" with "ect", which should be "ec".
There is another sheet which shows another approach. This is an excerpt from a letter of 23 November 1782 from Livingston to Jay (see here for the relevant text in cipher and in clear).
This letter contains two blocks written in code, the second of which corresponds to this excerpt. The code and the plaintext are shown below.
Below the coded text, the code numbers used in this paragraph are listed in the numerical order and given reconstructed readings. Convention of representing trailing "e" or "s" by a dot was not recognized. Thus, code numbers such as 19, 42, 55, etc. are given double readings with and without the trailing "e" or "s". For example, 19 is given "th" and "the", 42 is given "e" and "es", and 55 is given "c" and "ce".
This code (TH=19', WE008) was first sent by Robert Morris to Benjamin Franklin in Paris in July 1781 and later shared with Jay after he joined Franklin in June 1782 (see here). It was mainly used in 1781-1783.
Jefferson was sent to Paris to assist Franklin and worked with him from his arrival in August 1784 to July 1785, when Franklin left for America. Apparently, Jefferson did not take over code from Franklin and THE=19' (WE008) is not one of many codes he used during his residence in Paris (see here). Anyway, if the date 1794 is correct, Jefferson was out of office at the time and may not have access to the code.
Jefferson had once successfully identified correspondence between a code and its severely corrupted copy. When he left for France, his friend James Monroe gave him a code (WE019, THE=907). Monroe's subsequent letters in that code, however, could not be decoded. After many months' frustration and several weeks' work in January 1785, Jefferson could read Monroe's letter. (See here for details.)
Surviving documents do not show his success for THE=19' (WE008).