How can I convert my list of lists to fixed size matrix?

I want to create Hemming Matrix. I have just built Galois field like multiplicative group. That's what I got:

MultiplicativeGroup = DeleteDuplicates[
   NestList[
    PolynomialMod[
      PolynomialMod[(generating*#), irreducablePolynomial], 2] &, 1, 
    n]];

{1, a, a^2, 1 + a^2, 1 + a + a^2, 1 + a, a + a^2}

After that I converted it into binary form which look like this one:

CoefficientList[MultiplicativeGroup, a]

{{1}, {0, 1}, {0, 0, 1}, {1, 0, 1}, {1, 1, 1}, {1, 1}, {0, 1, 1}} But I stuck with converting it into binary matrix form. It's have to look like this one:

(0  0   1   1   1   0   1
0   1   0   0   1   1   1
1   0   0   1   1   1   0)

But I actually don't know how to do it. I can't transpose it or do anything else. Could you help me?