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

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+28x^26+454x^28+28x^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 0.031 seconds.