The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+252x^26+128x^27+359x^28+32x^29+188x^30+32x^31+22x^32+8x^34+1x^36+1x^40

The gray image is a code over GF(2) with n=224, k=10 and d=104.
This code was found by Heurico 1.16 in 0.031 seconds.