The generator matrix

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

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+166x^20+24x^21+344x^22+152x^23+650x^24+336x^25+782x^26+336x^27+634x^28+152x^29+318x^30+24x^31+141x^32+26x^34+8x^36+2x^38

The gray image is a code over GF(2) with n=104, k=12 and d=40.
This code was found by Heurico 1.16 in 0.436 seconds.