Answer: The inference is supported by the excitement the men feel when they discover that the message was sent by Zimmermann, the German foreign secretary.
This excerpt indicates to us that the men were trying to decipher a very important message. We know this for several reasons. We are told that the 90000 family indicates important names that are not used often, and this code was used in the message. We also know that the men were "shocked" when they linked the code to Zimmerman, and excitement grew as they worked on it. All of this shows the importance of this message.