The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+83x^20+200x^22+408x^24+682x^26+406x^28+182x^30+55x^32+22x^34+7x^36+2x^38

The gray image is a code over GF(2) with n=104, k=11 and d=40.
This code was found by Heurico 1.16 in 0.0934 seconds.