The generator matrix

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

generates a code of length 28 over Z2[X]/(X^4) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+32x^26+48x^27+350x^28+48x^29+32x^30+1x^56

The gray image is a linear code over GF(2) with n=224, k=9 and d=104.
This code was found by Heurico 1.16 in 0.016 seconds.