The generator matrix

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

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+310x^22+422x^24+618x^26+430x^28+202x^30+41x^32+22x^34+2x^36

The gray image is a code over GF(2) with n=104, k=11 and d=44.
This code was found by Heurico 1.16 in 17 seconds.