The generator matrix

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

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+132x^24+192x^25+608x^26+576x^27+1090x^28+576x^29+608x^30+192x^31+109x^32+6x^36+6x^40

The gray image is a code over GF(2) with n=224, k=12 and d=96.
This code was found by Heurico 1.16 in 0.078 seconds.