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

generates a code of length 28 over Z4[X]/(X^3+2,2X) 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 18.4 seconds.