The generator matrix

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

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+97x^24+550x^25+1179x^26+1448x^27+1913x^28+1292x^29+966x^30+488x^31+170x^32+46x^33+23x^34+16x^35+3x^36

The gray image is a code over GF(2) with n=224, k=13 and d=96.
This code was found by Heurico 1.16 in 0.25 seconds.