The generator matrix

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

generates a code of length 28 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+200x^24+184x^26+256x^27+786x^28+256x^29+192x^30+141x^32+8x^34+22x^36+2x^40

The gray image is a linear code over GF(2) with n=224, k=11 and d=96.
This code was found by Heurico 1.16 in 0.765 seconds.