The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+580x^24+368x^28+75x^32

The gray image is a code over GF(2) with n=104, k=10 and d=48.
This code was found by Heurico 1.16 in 38.8 seconds.