The generator matrix

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

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+568x^24+964x^26+1128x^28+872x^30+463x^32+84x^34+16x^36

The gray image is a code over GF(2) with n=112, k=12 and d=48.
This code was found by Heurico 1.11 in 10.1 seconds.