Why not do it using audio modem software over a phone call ... might be able to reach higher speeds - approaching 56kbps??
While there are higher bitrate codecs, a full-rate GSM channel is only about 13 kbps, and depending on radio conditions the voice data may be compressed down to half that or even less.
For comparisons, when landline connections are digitised, it is typically compressed to a 56kbps or 64kbps channel.