Codina was born in 1988 in Barcelona (Spain) and began studying the cello at the age of five with Eulalia Subirà. Other teachers to date have included Ivan Chiffoleau, Daniel Grosgurin, Peter Thiemann and Louise Hopkins. He graduated from the Yehudi Menuhin School in 2006, and from the Guildhall School of Music & Drama with first class honours in 2010. He later obtained a Solo Artist Diploma from the Chapelle Musicale Reine Elisabeth, where he studied with Gary Hoffman.

He has also performed extensively throughout Spain, England and Germany, in venues such as the Wigmore Hall, the Royal Festival Hall, the Purcell Room, the Pau Casals Auditorium, L’Auditori de Barcelona and the Palau de la Musica Catalana Concert Hall in Barcelona. He has appeared as a soloist with several orchestras such as the Barcelona Symphony Orchestra, the Empordà Chamber Orchestra, the Andorra Chamber Orchestra, the Südwestdeutsches Kammerorchester Pforzheim, the Franz Liszt Chamber Orchestra of Budapest, the Chamber Orchestra of Wallonie, the RTVE Orchestra in Madrid and the Orquestra Simfònica del Vallès.