The generator matrix

 1  0  0  1  1  1  2  1  1  1 X^2+X  1 X^2 X^2+2  1  X  1  1 X+2  1  1  1 X^2+X X^2+X X^2+X  1  2  1
 0  1  0  2 X^2+1 X^2+3  1 X^2 X^2+2  1  1 X^2+X+3  1 X^2+X  3  1 X^2+X  X  1 X+3 X+2 X+1  0 X^2+X  1 X+1  1 X+2
 0  0  1 X+3 X+1  2 X^2+X+1  X  3  1 X^2 X^2 X^2+1  1 X^2+X X^2+1 X^2+X+1  X X^2+X+1 X+1 X^2+1 X^2+X+2  1  1 X^2+X+2 X^2+3 X^2+X  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+1428x^26+1456x^28+1008x^30+175x^32+28x^34

The gray image is a code over GF(2) with n=224, k=12 and d=104.
This code was found by Heurico 1.16 in 13.5 seconds.