What is known about the plethysm $\text{Sym}^d(\wedge^3 \mathbb{C}^6)$ as a representation of $\text{GL}(6)$? It is my understanding that this should be multiplicity-free. I tried computing it using the Schur Rings package in Macaulay2 and I cannot see a pattern among the weights that appear.

If a formula is known, a reference would be nice also. Thanks.