The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+46x^24+288x^25+617x^26+764x^27+855x^28+662x^29+478x^30+202x^31+104x^32+58x^33+9x^34+10x^35+1x^36+1x^40

The gray image is a code over GF(2) with n=224, k=12 and d=96.
This code was found by Heurico 1.16 in 0.078 seconds.