The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+418x^22+1868x^23+5877x^24+14580x^25+30544x^26+49146x^27+56763x^28+49762x^29+30810x^30+14452x^31+5734x^32+1672x^33+372x^34+98x^35+37x^36+2x^37+4x^39+4x^40

The gray image is a code over GF(2) with n=224, k=18 and d=88.
This code was found by Heurico 1.16 in 212 seconds.