In Neri et al. (2022) [20], the authors extended the family of 2-dimensional Fq2t-linear MRD codes recently found in Longobardi et al. (2023) [13]. Also, for t≥5 they determined equivalence classes of the elements in this new family and provided the exact number of inequivalent codes in it. In this article, we complete the study of the equivalence issue removing the restriction t≥5. Moreover, we prove that in the case when t=4, the linear sets of the projective line PG(1,q8) ensuing from codes in the relevant family, are not equivalent to any one known so far.