The generator matrix

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

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+112x^25+315x^26+450x^27+350x^28+424x^29+275x^30+84x^31+8x^32+8x^33+9x^34+10x^35+1x^38+1x^40

The gray image is a code over GF(2) with n=224, k=11 and d=100.
This code was found by Heurico 1.16 in 0.015 seconds.