The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+99x^24+136x^25+178x^26+432x^27+376x^28+464x^29+134x^30+112x^31+88x^32+8x^33+6x^34+11x^36+2x^38+1x^44

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.