I don’t know if this approach will work or not. My idea was that when we deal with images, the data comes in shape (height, width, n_channels). Here we have data in shape (8, 8, n_classes). Probably, you can try some transformer based models similar to those that are applied for image classification but adjust them to your problem. You can find some examples of image transformers at keras.io.
Other possible solution could be to flatten the input data as if you deal with a 64 word-long sentence. Use ordinal encoder for classes in this case. So you will have a sequence of 64 digits and will be able to use models similar to text classifiers.