The generator matrix

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

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+101x^22+952x^23+3031x^24+7594x^25+15048x^26+24132x^27+29068x^28+24422x^29+15387x^30+7508x^31+2678x^32+894x^33+210x^34+30x^35+6x^36+2x^37+6x^38+2x^43

The gray image is a code over GF(2) with n=224, k=17 and d=88.
This code was found by Heurico 1.16 in 47.9 seconds.