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It does not seem to be supported. There is no support for submodules of $\mathbb{Z} / n \mathbb{Z}$

sage: F = Zmod(4)**3
sage: v0 = F((1,0,0))
sage: v1 = F((1,1,1))
sage: F.submodule([v0,v1])
Traceback (most recent call last):
NotImplementedError: Echelon form not implemented over 'Ring of integers modulo 4'.

There is an old ticket (#6452) on the Sage development website that aimed to implement it. There is some code with it but sadly not in final stage. If you have some programming skill you might have a look and contribute to Sage!