The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+26x^26+62x^27+83x^28+58x^29+13x^30+6x^31+4x^32+1x^34+2x^37

The gray image is a code over GF(2) with n=224, k=8 and d=104.
This code was found by Heurico 1.16 in 0.016 seconds.