The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1 2X+2  1  1  1  1 2X+2  1  1  1
 0  2  0  0  0 2X+2  2 2X+2  0 2X  2  2  0 2X  2  2  2  0 2X 2X  0  2 2X 2X  2  2  0  0
 0  0  2  0 2X+2 2X+2 2X+2 2X  0 2X 2X+2  2 2X+2 2X+2  2 2X+2 2X 2X+2  0  2 2X+2 2X  2 2X 2X+2  2 2X+2 2X+2
 0  0  0  2 2X+2 2X  2  2  0  2 2X  2 2X+2  0 2X+2 2X+2  2  2  2 2X+2  0  0  2 2X+2  2  2 2X 2X+2
 0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X  0  0 2X  0  0 2X  0 2X 2X 2X 2X  0  0

generates a code of length 28 over Z4[X]/(X^2+2X+2) 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 code over GF(2) with n=224, k=11 and d=96.
This code was found by Heurico 1.16 in 0.375 seconds.