The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+271x^24+72x^25+784x^26+480x^27+882x^28+624x^29+618x^30+96x^31+209x^32+8x^33+36x^34+10x^36+2x^38+3x^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 4.48 seconds.