He was engaged to a woman named Isabel Espinoza with whom he had a son called Domingo.
According to historian Diego Barros Arana the government of Barreda was as short and irrelevant.
During his government the cabildo of Santiago sent a request to the viceroy of Peru to have Mauricio de Zavala confirmed as governor of Barreda until the arrival of titular governor Bruno, who had to arrive to Chile through Buenos Aires.
The news about some Dutch ships which had cast anchor in the neighborhoods of Valdivia spread and they arrived to governor Barreda.
He inaugurated the Caja de Recogidas, a work begun by Gabriel Cano, in Santiago.