Jacquez's body was found about two miles north of NM 516 by a mountain biker shortly after 11:30 a.m. that day.
He was shot five times in the head, Sheriff's Lt. Cory Tanner said.
Deputies are looking for 22-year-old Gabriel Alcon, 20-year-old Richard Winters, 29-year-old Vincent Montoya and 26-year-old Sarah Martinez.
No arrests have been made in connection with Jacquez's shooting.
A Sheriff's Office spokeswoman declined to release specific information about the shooting, citing the ongoing investigation.
Investigators believe the involved parties are affiliated with gangs, but Tanner said the motivation behind the shooting likely was not gang related.
Detectives on May 29 executed a search warrant at a mobile home on Ruins Road in Aztec. They initially responded to the home looking for two people wanted for questioning bu,t after a four-hour impasse, realized no one was in the home.
Deputies arrested one man, 47-year-old Martin Martinez, for allegedly shooting at detectives while they were conducting surveillance in connection with Jacquez's shooting. He was charged with two counts of aggravated battery with a deadly weapon and tampering with evidence, Tanner previously said.
Detectives believe Martinez's actions were unrelated to Jacquez's death.
Jacquez made headlines in 2008 after he was acquitted of first-degree murder charged in connection with the shooting death of Carlos Escobar.
Authorities believe Escobar was murdered after he and Thomas Vigil, then 27, exchanged gunfire outside a county road residence south of Bloomfield on Oct. 21, 2005.
After the initial exchange, Escobar accelerated his pickup truck in reverse until he reached the roadway, where investigators believed Larry Abeyta, Jared Jacquez and Anthony Jacquez began shooting at the vehicle.
Anyone with any information is asked to contact the San Juan County Sheriff's Office Detective Division at 505-334-6107. Those who wish to remain anonymous can call San Juan County Crime Stoppers at 505-334-TIPS (8477) where they can receive a reward up to $1,000.