The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+41x^26+184x^27+58x^28+184x^29+42x^30+1x^34+1x^48

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 -3.24e-008 seconds.