The generator matrix

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

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+18x^26+220x^28+12x^30+3x^32+2x^42

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 0.141 seconds.