The generator matrix

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

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+176x^24+192x^26+256x^27+822x^28+256x^29+192x^30+126x^32+26x^36+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 0.391 seconds.