The generator matrix

 1  1  1  1  1  1  1  1  X  1  0  1  1  X X^3+X^2  1  1  X X^3  X X^2  1  1  1  X  X  X  X
 0  X X^3+X^2 X^2+X X^3 X^3+X^2+X X^2 X^3+X X^2+X  0  X X^2+X X^3+X^2 X^3+X  X X^3 X^2 X^3+X^2+X  X  X  X X^3+X^2+X X^3+X  X  0 X^3 X^3+X^2 X^2

generates a code of length 28 over Z2[X]/(X^4) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+120x^28+7x^32

The gray image is a linear code over GF(2) with n=224, k=7 and d=112.
As d=112 is an upper bound for linear (224,7,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 7.
This code was found by Heurico 1.16 in -6.48e-008 seconds.