Why not? "A code" is a software package which solves some kind of problem computationally. Plural, codes. I'm sure it's been in use almost as long as the programmable computers. Here's[1] a link to an article from 1968 which uses the term in the singular ("The MENE Neutron Transport Code".)
[1] https://www.osti.gov/biblio/4819611-mene-neutron-transport-c...
Then you probably haven't been around physicists, or read enough physics-related material. A non-scholarly reference which can't be easily checked online is George Dyson's "Project Orion," where Freeman Dyson (author's father) is quoted as mentioning this or that "code" as significant for the design of various Orion parts. (That should be a native enough English speaker.) The time-frame is late 1950s to early 1960s.
That reference you give doesn’t appear to be available online but I’ll take your word for it.
Obviously, what word they use for it is arbitrary but it's indicative of an actual problem - they're all totally cut off from the software engineering / CS community. Lots of them think programming is like learning to juggle or ride a bike or something, a skill that anyone just learns and then they're done. Then, obviously, they make major mistakes that invalidate their conclusions and nobody notices or cares because it's all student code, all the time.
I think the point is that the physicists were among the very early adopters of computing systems. I’m not sure about the history of the term “code” used this way, but it might literally predate compiled software since Ulam and von Neumann invented the Monte Carlo method in 1948 during the Manhattan Project.
Personally I think it just sounds outdated now, but it’s pretty common to hear people call their software “a hydrodynamics code” or “a molecular dynamics code”
The tendency is to call computational science software “codes”, but I’ve never heard a scientist call, ie a web browser, a code.
There’s a different connotation. Like how theres a different connotation between a program, an application, and and app. The are largely synonymous, but have slightly different uses.
See for example Code_Aster (as in, "a code"), which is one of the largest projects for open source FEA (and it mostly rooted in academia).