The generator matrix

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

generates a code of length 28 over Z4[X]/(X^3+2,2X) 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 1.05e-007 seconds.