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

generates a code of length 28 over Z4[X]/(X^2+2) 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 code over GF(2) with n=224, k=11 and d=96.
This code was found by Heurico 1.16 in 18 seconds.