I will try to revive Sagemath's ticket [#14110](https://trac.sagemath.org/ticket/14110) and provide a Sagemath package for this enumeration (in fact, the C code, corresponding to the paper [D. McKay and G. Brinkmann, Posets on up to 16 points, Order, 19 (2002) 147-179](https://doi.org/10.1023/A:1016543307592) -   (mostly) due to Gunter Brinkmann, which is using Brendan's McKay's nauty, is posted there.