Would that all such questions had such easy - and satisfactory - answers!
The kit you need is the one currently marketed by Revell Germany under the name "Harbour Tug Boat." It is in fact a reissue of a kit originally produced in 1956. It made its first appearance under the name Long Beach. I don't remember much about that TV show, but I think I recall reading elsewhere in this Forum that the tug in the show was a near-sister of the actual Long Beach. In its original packaging the kit decal sheet included the same device on the stack that's on the model in your photo.
It's an old kit, but in many respects a beauty - loaded with character and detail. The crew figures are especially nice. The scale is (according to Dr. Thomas Graham's book, Remembering Revell Model Kits) 1/108. That makes it a little bigger than 3/32"=1' (which is 1/128) - but not much.
The current issue of the kit is identical to the original except in a couple of minor respects. For a while Revell sold the kit with an electric motor, and the main deckhouse was held in place by a couple of screws to give access to the batteries. The current German release omits the motor, but the deckhouse sides have some big, mysterious-looking projecting lugs that used to slip under the heads of the screws. They can be sliced off in a couple of minutes. The other change is that the plastic parts, instead of the original light grey, are an alarmingly bright red. But you'd undoubtedly want to paint every square milimeter of it anyway.
It may be a little hard to find, but a decent hobby shop should be able to order it. (I found mine on the shelf of the Hungate's chain store here in Greenville, NC.) It's a nice old kit. Good luck.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.