I'm wondering if it is a European model? Looking at pics, it appears to have smaller bumper guards in the rear than the US models I've looked at. Though I'm not certain if the widebody package was available on the Targa models. It could be something heavily modified?

1984 was the first model year in the US for the Carrera, replacing the SC.

BTW, I tried the plate and nothing came up, which may support it being a Euro model. A 1984-1985 US model should have been accessible to Autocheck.