The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+328x^23+1729x^24+3846x^25+7933x^26+11384x^27+14811x^28+11872x^29+8128x^30+3496x^31+1458x^32+422x^33+105x^34+8x^35+9x^36+4x^37+2x^38

The gray image is a code over GF(2) with n=224, k=16 and d=92.
This code was found by Heurico 1.16 in 12.3 seconds.