The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1 2X  X  1  1  X  1  1 2X+2 2X  1  1  X  1  2
 0  X  0 3X+2  2 X+2 2X+2  X 2X  0  2  2 X+2 X+2  X 3X+2 3X+2 3X+2 X+2  X 2X  X  X 2X+2 2X+2  2  0 2X+2
 0  0 2X+2  0  2  0  0 2X  0  2  2 2X 2X 2X+2 2X+2  0  2 2X+2 2X+2  2 2X 2X 2X  0  2 2X 2X+2 2X
 0  0  0 2X+2  0  0 2X  2  2  2 2X+2  2 2X 2X+2 2X  2  0  2  2  2  2 2X 2X+2 2X  2 2X+2  2 2X
 0  0  0  0 2X 2X 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X  0 2X 2X  0 2X  0  0  0 2X 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+305x^24+64x^25+658x^26+448x^27+1189x^28+448x^29+652x^30+64x^31+204x^32+34x^34+27x^36+2x^40

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 47.8 seconds.