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  X  X  X  X
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2  0 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^2  0 X^3  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2
 0  0 X^3  0  0  0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3
 0  0  0 X^3  0  0  0 X^3  0  0  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 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  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3
 0  0  0  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0
 0  0  0  0  0  0 X^3  0 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 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+209x^24+1632x^28+202x^32+3x^40+1x^48

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 17.9 seconds.