The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  1  X  1  X  1  1  X 2X+2  1  1  1
 0  X  0  X 2X  0 3X+2 X+2  0 2X 3X 3X  0  2 X+2  2 2X+2 3X  X 3X 3X+2 X+2 3X X+2  X X+2  0 2X+2
 0  0  X  X  0 X+2 3X+2 2X 2X+2 X+2 X+2 2X+2  2  X 2X+2 3X  X 3X X+2 2X 2X+2  0 2X X+2 3X  X 3X 3X+2
 0  0  0 2X+2  2 2X+2 2X 2X+2 2X+2  0 2X+2  2  0  2  0 2X  2  0 2X+2  2  2 2X 2X 2X+2 2X+2 2X+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+174x^24+228x^25+450x^26+832x^27+857x^28+760x^29+366x^30+192x^31+165x^32+36x^33+30x^34+2x^36+2x^38+1x^44

The gray image is a code over GF(2) with n=224, k=12 and d=96.
This code was found by Heurico 1.16 in 0.141 seconds.