In this grasshopper example file by defining a closed polyline and using the Kangaroo plugin you can create a parametric minimal surface.
In this paper, Eike Schling aims at strained gridshells built entirely from straight or circular lamellas of the same radius and with orthogonal nodes. The lamellas are aligned normal to a reference surface, enabling an elastic assembly.
Minimal Surface Creator by Cerver is a grasshopper plugin that generates minimal surfaces from boundary curves or do a minimal relaxation on a mesh.
In this grasshopper definition by using standard minimal surface equations, you can create different minimal surfaces and also use Align vertices to avoid generating an invalid mesh.