Conjecture on the range of topological conformal dimension

The topological conformal dimension of a metric space $X$ is

$$\dim_{tC}X = \inf\{d: X\text{ has a basis }\mathcal{U}\text{ such that }\dim_C \partial U \leq d-1\text{ for all }U\in\mathcal{U}\}.$$

Range conjecture. For every $d\in[2,\infty]$ there is a metric space $X$ with

$$\dim_{tC}X=d.$$

Determining the range of topological conformal dimension is open; it is known that $\dim_{tC}X\in\{-1,0,1\}\cup[2,\infty]$, but it is unknown whether every value in $[2,\infty]$ is attained.