The quality to which a unique six-character code is assigned in graphic design is called a "HUE." This refers to the quality of a color as determined by its dominant wavelength, and the term "hue" is used to specify a particular shade or tint in color theory. In the context of the New York Times crossword puzzle, the answer to this clue was "HUE".

Additionally, the phrase "Possesses a certain unnameable quality" from a recent NYT crossword clue refers to "HASIT," which is an informal way to describe someone or something having an intangible, special, or magnetic quality often called the "X-factor".