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 X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2 X+2  0 X^2+X  2 X^2+X+2 X^2+2 X^2 X^2+X+2 X+2  2  X X^2 X^2+X
 0  0  2  0  0  2  2  2  2  0  0  2  2  2  0  0  2  2  2  0  0  0  2  0  0  2  2  0
 0  0  0  2  2  2  2  0  2  0  0  2  0  0  2  2  0  0  2  2  2  0  2  0  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+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 0.015 seconds.