The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+200x^25+774x^26+792x^27+880x^28+540x^29+524x^30+228x^31+111x^32+28x^33+14x^34+4x^35

The gray image is a code over GF(2) with n=224, k=12 and d=100.
This code was found by Heurico 1.16 in 0.062 seconds.