The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+524x^22+960x^24+1184x^26+936x^28+396x^30+87x^32+8x^34

The gray image is a code over GF(2) with n=104, k=12 and d=44.
This code was found by Heurico 1.16 in 90.5 seconds.