The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  1  2  1  1  0  X  1  1  1  1  X
 0  X  0  0  0  X X+2  X  0  2  X X+2  0  2  X  2  2  X  0  0  0  X  2 X+2 X+2  2  0  X
 0  0  X  0  X  X  X  2  0  2 X+2 X+2  X  X  2 X+2  X  2  X  2  0  0  0 X+2  2  X  2  X
 0  0  0  X  X  2 X+2 X+2  0 X+2  2 X+2  X  0  X X+2 X+2  0 X+2  2  X  0  X  X  X  0 X+2  2
 0  0  0  0  2  2  2  2  2  2  0  0  0  2  0  2  0  2  2  0  2  2  0  2  2  0  2  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+158x^24+64x^25+192x^27+221x^28+192x^29+64x^31+103x^32+26x^36+2x^40+1x^44

The gray image is a code over GF(2) with n=112, k=10 and d=48.
This code was found by Heurico 1.16 in 0.14 seconds.