The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1  2  1  1  0  1  X  1  1  1  1  1  0  1  1  1  1  2
 0  1  1  0 X+3  1  2 X+3  1  X X+1  1  0  3  1 X+2  1 X+3 X+2  1  0 X+2  1  1 X+2 X+2  2  1
 0  0  X  0 X+2  2  X  0  X  0  2  0 X+2  X X+2  X  0  X  2  2  2 X+2  2  2 X+2 X+2  0  2
 0  0  0  X  0  2  0 X+2 X+2  X  2 X+2  X  X  2  2  X X+2  0 X+2  0  0  0  2 X+2  X  X  X
 0  0  0  0  2  2  2  2  0  2  0  2  2  2  2  0  0  0  0  2  2  0  2  0  0  2  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+269x^24+448x^26+642x^28+448x^30+207x^32+30x^36+3x^40

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 24.3 seconds.