The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  X  1  X  X
 0  2  0 2X+2  0 2X  2  2  0 2X 2X+2  2  0  0  2  2 2X 2X+2  2 2X  0 2X 2X  0  2 2X+2 2X+2  2
 0  0  2 2X+2  0 2X+2 2X+2 2X  0 2X+2 2X+2  0  0  2 2X+2 2X 2X  2  2 2X+2  2  2  0 2X 2X  0  2  0
 0  0  0 2X  0  0 2X  0 2X 2X  0 2X 2X 2X  0 2X 2X 2X  0  0  0  0 2X 2X  0  0  0  0
 0  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0  0 2X  0 2X  0  0  0 2X  0  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 24.

Homogenous weight enumerator: w(x)=1x^0+42x^24+8x^25+89x^26+56x^27+661x^28+56x^29+58x^30+8x^31+22x^32+13x^34+9x^36+1x^48

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.