The salmon GH gene was cloned from coho salmon already in 1985 (Sekine et al Proc. Nati. Acad. Sci. USA Vol. 82, pp. 4306-4310, July 1985) and since, the GH sequences of the two salmonid GHs have been cloned in several salmonid species. The easiest way for you to find these sentences is through GeneBank.

The GH gene is primarily expressed in the pituitary gland, so that's the tissue you want to work with, not blood or brain.

I attach two publications from my group where GH expression has been studied in Atlantic salmon, during sexual maturation and smoltification, respectively, but there are a lot of other published papers studying GH gene expression in various other salmonid species.

Article Pituitary and plasma growth hormone dynamics during sexual m...

Article Pituitary gene expression of somatolactin, prolactin, and gr...