0001 0001 0001 0001
Source: Original.
There are 10 basic solutions, each of which has 15 of the 16 possible 4-bit patterns. (A grid with all 16 is impossible.) Rotating, reflecting, or exchanging 1s with 0s will find the rest of the 160 possible solutions. Many thanks to Carlos Rivera for finding these 10 solutions.
0001 0101 1111 1001 | 0001 0110 1100 1101 | 0001 0111 1100 1001 | 0001 0111 1101 1001 | 0001 1010 0110 1011 | 0001 1010 0111 1001 | 0001 1010 1111 1001 | 0001 1011 0111 1001 | 0001 1111 0011 1001 | 0001 1111 1100 1001 |
Several solvers suggested a quick follow-up puzzle to find the grids in which only 2 unique 4-bit patterns can be found. (There are only 4.)