The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  1  X X^2
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^2 X^3+X^2  0 X^3+X^2 X^3+X^2  0  0 X^3 X^3+X^2 X^3 X^3+X^2
 0  0 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3  0 X^3+X^2 X^2  0 X^2 X^2  0 X^3+X^2 X^2 X^3  0 X^3 X^3  0 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+26x^26+62x^27+83x^28+58x^29+13x^30+6x^31+4x^32+1x^34+2x^37

The gray image is a linear code over GF(2) with n=224, k=8 and d=104.
This code was found by Heurico 1.16 in 0.015 seconds.