The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X 2X+2  1  X  1  1  X  1  1  1
 0  X  0  X 2X  0 3X  X  2 X+2  2 X+2 2X+2  2 3X+2 X+2  0 2X  X  X 2X 3X+2  0 2X+2  X  2 X+2 2X
 0  0  X  X  2 X+2 X+2  2  2 3X+2  X 2X  0 X+2 3X 2X+2 2X 3X+2  2 3X+2 3X 2X+2  2  X 3X  0  0 2X

generates a code of length 28 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+64x^25+114x^26+202x^27+296x^28+186x^29+89x^30+50x^31+6x^32+6x^33+4x^34+4x^35+1x^38+1x^48

The gray image is a code over GF(2) with n=224, k=10 and d=100.
This code was found by Heurico 1.16 in 0.015 seconds.