The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+164x^23+822x^24+1884x^25+3937x^26+6070x^27+7099x^28+5990x^29+4044x^30+1792x^31+667x^32+216x^33+65x^34+6x^35+3x^36+6x^37+2x^38

The gray image is a code over GF(2) with n=224, k=15 and d=92.
This code was found by Heurico 1.16 in 3.73 seconds.