The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  X  1  1  0  1 2X 2X+2  X 2X 2X+2  1
 0  X  0  X 2X  0 3X+2 3X+2 2X+2 2X+2 X+2  2 3X+2  0 X+2 3X+2  X 3X  2  2  X 2X+2  X  X 3X  X  X  0
 0  0  X  X 2X+2 3X+2 3X+2  0  2  X 2X+2 3X 2X  X 3X 2X 3X+2 X+2  0 X+2 X+2 X+2  2  X  X  2 X+2  0
 0  0  0 2X 2X 2X  0 2X  0  0 2X  0 2X 2X  0  0  0 2X  0 2X 2X  0  0  0 2X 2X  0  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+35x^24+208x^25+274x^26+422x^27+262x^28+390x^29+190x^30+166x^31+50x^32+26x^33+14x^34+4x^35+4x^36+2x^38

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 0.031 seconds.