Though this isn't an Android-related issue in my case I'm replying here as this page has a pretty high search engine rank for the query and I haven't yet found a similar thread on AT&T help forums etc.
I also received a Multimedia Message from the 7700 short code at 09:06 EST on 21 November 2013. There was no plain text data included as a body or subject line, and when I've attempted to access the MMS file itself (reported to be "32 KB" in size) the network has each time eventually responded that it was "unable to retrieve message", after a minute or two of presumably trying to access it.
I've successfully received image files recently on this same device and subscription plan so I don't think it's failed simply because I can't receive such messages generally.
I guess if the sender has been spamming they might have had their network-stored MMS files deleted by the carrier but still for a time retained the ability to send it could be some sort of network error.
Per
Short code - Wikipedia, the free encyclopedia , cross-carrier uniformity of reference is only implemented in the US for codes of five or more digits, and though indices like
Common Short Codes | Get a Short Code & Grow Mobile Marketing Revenue apparently list the registrants of 'common'/compatible-among-different-carrier-networks short codes, they don't list those that are carrier-specific.
My configuration for reference:
LG device model LGC395;
software revision LGC395-V10i-APR-05-2013-ATT-US;
operating system Brew MP version 1.0.4;
network service via AT&T