[Edit: correct spelling in my comments.)
You need to use the transpose of the data array. pwelch() finds the spectrum of each column, when the input data is an array. And in your array, the data whose spectra you wish to compute are in rows. See the following, which runs without error.
SuperTrialH2Hit=rand(30,207701);
SR=1; % sampling rate
segment_length = 1229;
hannw = hann(segment_length);
overlap_length = round(segment_length / 2);
disp(size(SuperTrialH2Hit))
[pxx4HH, hz4HH] = pwelch(SuperTrialH2Hit', hannw, overlap_length, ...
nextpow2(numel(SuperTrialH2Hit)), SR);
Good luck.
