The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+527x^24+952x^25+2164x^26+2760x^27+3620x^28+2808x^29+2144x^30+856x^31+445x^32+48x^33+44x^34+12x^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 1.84 seconds.