Finite excluded-minor characterization conjecture for codes over finite fields

Let ${\mathfrak C}$ be a minor-closed class of codes over a finite field ${\mathbb F}$. For a collection ${\mathcal F}$ of codes, let ${\mathfrak C}_{\mathcal F}$ denote the class of codes having no minor equivalent to a member of ${\mathcal F}$. Finite excluded-minor characterization conjecture. There is a finite collection of codes ${\mathcal F}$ such that

$${\mathfrak C}={\mathfrak C}_{\mathcal F}.$$

Thus every minor-closed class of codes over a finite field should be characterized by a finite list of excluded minors. The conjecture extends the binary-code formulation to arbitrary finite fields; the source gives no resolution status.