Not many builds for decent sentinel weapons, so here's one that does something useful for spreading statuses.
[Nautilus] loves this weapon with its pull mod, [Cordon].

This is good for putting the hurt on low level enemies and spreading status on higher level enemies as well as stunning, burning, staggering, and reducing health of enemies it hits.

Shots fired will cause a status proc 100% of the time for each projectile. Though this weapon only fires 4 projectiles - along with multishot, a possible of 12 total - at a time, I have noticed anywhere between 10 and 18 of varying procs per burst shot on average as shown in the video below.

[Rifle Aptitude] is used instead of [Galvanized Aptitude] because it, combined with a Rank 2 [Malignant Force] and [Rime Rounds], allows for the status chance to stay above 100% while also making heat have more damage weight than viral, allowing it to hit more often.

The Vigilante mods are there for you to benefit from the set effect. Only 2 of 4 Vigilante mods work in favor of the status-spreading mechanism. If you really want those last Vigilante mods though, then the only mods you could swap out are [Vile Acceleration] and [Galvanized Chamber]. For the 100% status chance, there is no other way (unless you have a riven).

Desirable riven stats would be along the lines of status chance, multishot, fire rate, and maybe projectile speed (if you can't get the first three together) to make up for some shortcomings and possibly free up another space.

It should be noted that in higher level missions, Galvanized Aptitude really doesn't help that much other than the status chance (the damage against enemies becomes almost non-existent). If you do intend to get a riven, [Rifle Aptitude] or [Galvanized Chamber] are the mods you'd want to replace.

The [Thermite Rounds] is good for CC'ing a small area and can be swapped out for [High Voltage] if you prefer a small AoE CC without DoT. It is worth noting that the fire rate increase from Vigilante Fervor makes the sentinel fire just after the Burn/Stun status effect ends for most lower level enemies, so it will nearly constantly cc a single target or small group.

To add to this, using [Thermite Rounds] for heat procs will double the heat damage you do on radial attacks (giving it an even higher chance to proc heat over the other statuses) while adding [High Voltage] causes both Electricity and Radiation to proc from direct hits and radial hits respectively. This is because the radial damage has innate heat, while the direct shot does not.

Hope this helps! Would love to see feedback on your builds and recommendations!

Related Build:
Actually Useful Sentinel Status Weapon (w/o Vigi Mods)

Edit: Swapped out [Split Chamber] for [Galvanized Chamber] (Slight chance of getting more multishot in exchange for .1 more from [Split Chamber]).
Edit: Swapped out [Vigilante Offense] for [Primed Fast Hands] as Punch Through does not seem to work on this weapon. It also significantly benefits from reload speed.
Edit: Upon further testing, I have noticed that fire rate actually effects the "reload" period for the weapon, so I have added [Vile Acceleration] instead of [Primed Fast Hands].