The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+28x^27+84x^28+8x^30+3x^32+4x^35

The gray image is a code over GF(2) with n=224, k=7 and d=108.
This code was found by Heurico 1.16 in 0.032 seconds.