The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X 2X+2 X+2  0 X+2 2X+2 3X  0 X+2 2X+2 3X 2X 3X+2  2 3X  0 X+2 2X 3X+2 2X+2  2 3X+2 3X 2X  X  2 X+2
 0  0 2X  0  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X  0  0 2X 2X  0
 0  0  0 2X 2X 2X 2X  0 2X  0  0 2X  0  0 2X 2X  0  0 2X 2X 2X  0 2X  0 2X  0  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+36x^26+32x^27+374x^28+32x^29+36x^30+1x^56

The gray image is a code over GF(2) with n=224, k=9 and d=104.
This code was found by Heurico 1.16 in 0.016 seconds.