The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X X^3+X^2  X  X  X X^3+X^2  X  X  X  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2 X^3+X X^3 X^3+X^2+X X^2  X X^2+X  X X^3+X  X  0 X^3+X^2 X^2+X  X X^3+X X^3+X^2+X  0 X^3+X^2
 0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 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+29x^26+72x^27+45x^28+82x^29+17x^30+4x^31+2x^32+2x^33+2x^34

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.