The generator matrix

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

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+57x^24+78x^26+64x^27+129x^28+64x^29+68x^30+30x^32+14x^34+6x^36+1x^52

The gray image is a code over GF(2) with n=112, k=9 and d=48.
This code was found by Heurico 1.16 in 0.0125 seconds.