The generator matrix

 1  0  0  1  1  1 2X+2  0 2X 2X+2  1  1  1  1  1 3X+2 3X+2  1  1  1  X  X  1  1  1  0  1  1
 0  1  0  2  3  1  1 X+2  1  1 2X+2 X+2 2X+1 3X+3 2X+3  1  1  X 3X+3 3X  X 2X+2 2X+2 X+2 3X+1  1  2  0
 0  0  1 X+3 X+1  2 X+1  1 3X+2 2X+1 X+2  3  3  0 3X 3X  1 3X X+1 2X+2  1  1 2X+3 3X+3  1 2X  1  0
 0  0  0 2X 2X  0 2X 2X 2X  0  0  0 2X 2X  0 2X  0 2X  0  0  0  0 2X 2X 2X 2X 2X 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+114x^24+562x^25+1103x^26+1470x^27+1938x^28+1312x^29+944x^30+492x^31+168x^32+54x^33+17x^34+14x^35+2x^36+1x^40

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.