The generator matrix

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

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+539x^24+832x^25+2352x^26+2664x^27+3768x^28+2600x^29+2248x^30+760x^31+513x^32+56x^33+40x^34+8x^36+3x^40

The gray image is a code over GF(2) with n=224, k=14 and d=96.
This code was found by Heurico 1.16 in 1.86 seconds.