The generator matrix

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

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+74x^25+52x^26+174x^27+484x^28+136x^29+24x^30+32x^31+11x^32+30x^33+3x^34+2x^35+1x^50

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 0.11 seconds.