The generator matrix

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

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+586x^24+904x^26+1202x^28+816x^30+517x^32+40x^34+30x^36

The gray image is a code over GF(2) with n=112, k=12 and d=48.
This code was found by Heurico 1.16 in 58 seconds.