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When the particular dairy is not displayed on the bottle directly, it may mean the bottle is simply a generic milk bottle not assigned to a specific dairy. Therefore, mass-produced and cheaper for the dairy to purchase. The code M 3238-S may simply be the bottle code not a dairy code.
When the milk bottles were made with the particular dairy emblazened on them, it was usually obvious enough which dairy it was that a particular code would not be necessary.
Here's a bottle just like yours; only difference I can see is the embossed number on the bottom; yours is M-3238-S, other is M-3238-C. No maker's name shown. Perhaps you can contact the seller for more info. See link.