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^2+2  0 X^2  0  0 X^2 X^2+2  0 X^2  2 X^2 X^2+2  2  0 X^2+2  2 X^2+2  2  2 X^2 X^2+2 X^2  2 X^2  0  2 X^2+2
 0  0 X^2+2 X^2  0 X^2+2 X^2  0  2 X^2+2 X^2  0 X^2+2 X^2+2  2  2  2 X^2+2 X^2  0  0 X^2  2  2 X^2+2 X^2 X^2+2  2
 0  0  0  2  2  2  0  2  2  2  0  0  0  2  0  2  0  2  2  2  2  0  2  2  0  2  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+28x^26+454x^28+28x^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 0.031 seconds.