The generator matrix

 1  0  0  1  1  1 2X  1  1  1  1  X 3X+2 3X  1  1 3X+2  1 2X+2 3X+2  1  0  1 2X  1  2  1  1
 0  1  0 2X  3 2X+3  1  2 X+2 3X+1 2X+1  1 3X  1 3X X+3  1 X+2  1 2X+2 3X+3 X+2 2X+3  1  0  X  1  2
 0  0  1 3X+1 X+1 2X X+1  X  3 2X+2 2X+1 2X+2  1 2X+1 X+2 X+3 X+3 3X+1 X+2  1 3X+2  1  X  3  3  1  2 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+208x^25+774x^26+722x^27+992x^28+508x^29+489x^30+230x^31+134x^32+24x^33+9x^34+4x^35+1x^36

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 0.063 seconds.