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  X  X X^2
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0  0 X^3  0 X^3  0 X^3 X^3+X^2
 0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0
 0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3  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+24x^26+64x^27+76x^28+64x^29+22x^30+3x^32+2x^38

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.