The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+163x^24+236x^25+248x^26+336x^27+237x^28+228x^29+214x^30+156x^31+120x^32+64x^33+32x^34+4x^35+7x^36+2x^38

The gray image is a code over GF(2) with n=112, k=11 and d=48.
This code was found by Heurico 1.16 in 0.066 seconds.