Pyth, score = 2160 (10 bytes · 216)
sm+d+4d.p4
How it works
m .p4 map over all permutations d of [0, 1, 2, 3]:
+d+4d d + [4] + d
s concatenate
sm+d+4d.p4
m .p4 map over all permutations d of [0, 1, 2, 3]:
+d+4d d + [4] + d
s concatenate