MQTT and IR code Raw
First create a topic and include the ESP8266 ID. Do not make it part of the published value. 

Second publish the raw data as-is, uint16_t raw_ir_code[RAW_IR_CODE_MAX]. The alternative is to convert to string (characters). But if the subscriber has the same architecture (interpretation of data), there is no need to convert it to string and back. Simply publish the raw data as it is. 

You will need to cast the raw_ir_code vector to the appropriate type for the MQTT publish call. 

Cheers!