The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  X 2X+2
 0  2  0  2  0  2  0  2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2  2  2  2 2X+2  0  0 2X  0 2X  0 2X  2
 0  0 2X  0  0 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X  0 2X 2X 2X 2X  0  0  0
 0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X 2X  0  0  0 2X  0

generates a code of length 28 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+24x^26+64x^27+76x^28+64x^29+22x^30+3x^32+2x^38

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 0.016 seconds.