Not quite a one-liner in this form, but 2024 is the 22nd tetrahedral number.
tet = {{-11, -11, 11}, {-11, 11, -11}, {11, -11, -11}, {11, 11, 11}};
pick = Select[Tuples[Range[-12, 12], {3}],
OddQ[Total[#]] && Total[#] != -11 &&
Min[ResourceFunction["Areal"][tet, #]] >= 0 &];
Graphics3D[Sphere[#, 1/Sqrt[2]] & /@ pick, Boxed -> False]
Here's a check:
Total[Table[n (n + 1)/2, {n, 1, 22}]]
