The simplest way is to do:
CODE_DIR = code
.PHONY: project_code
project_code:
$(MAKE) -C $(CODE_DIR)
The .PHONY rule means that project_code is not a file that needs to be built, and the -C flag indicates a change in directory (equivalent to running cd code before calling make). You can use the same approach for calling other targets in the code Makefile.
For example:
clean:
$(MAKE) -C $(CODE_DIR) clean