The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+56x^26+4x^28+3x^32

The gray image is a code over GF(2) with n=104, k=6 and d=52.
This code was found by Heurico 1.16 in 0.00277 seconds.