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

generates a code of length 28 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+45x^24+120x^26+659x^28+128x^29+16x^30+30x^32+24x^34+1x^52

The gray image is a code over GF(2) with n=224, k=10 and d=96.
This code was found by Heurico 1.16 in 0.031 seconds.