The generator matrix

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

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+46x^24+210x^25+235x^26+296x^27+488x^28+342x^29+196x^30+152x^31+37x^32+22x^33+16x^34+4x^36+2x^37+1x^42

The gray image is a code over GF(2) with n=224, k=11 and d=96.
This code was found by Heurico 1.16 in 0.047 seconds.