The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X X^2+2  X  X  X X^2+2  X  X  X  1
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2 X+2  2 X^2+X+2 X^2  X X^2+X  X X+2  X  0 X^2+2 X^2+X  X X+2 X^2+X+2  0 X^2+2
 0  0  2  2  2  0  0  2  2  2  0  0  0  0  2  2  0  2  2  0  2  2  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+29x^26+72x^27+45x^28+82x^29+17x^30+4x^31+2x^32+2x^33+2x^34

The gray image is a code over GF(2) with n=224, k=8 and d=104.
This code was found by Heurico 1.16 in 0.015 seconds.