The generator matrix

 1  0  0  0  1  1  1  2  0  1  1  X  1  1  1  1  2  1 X+2 X+2  2  1  2  1  1  0
 0  1  0  0  0  1  1  1  1 X+2  X X+2 X+3  3 X+2  X  2 X+1  1  0  1 X+1  0  2  0  1
 0  0  1  0  1  1  0  3 X+1  2  3  1 X+1  0 X+2 X+1  X  X  2  1  1  2  1 X+2  0  X
 0  0  0  1  1  0  1  1  2 X+1 X+2  3  1  0 X+1  1  1 X+1 X+3  1 X+1 X+2 X+2  2  2  0
 0  0  0  0  2  0  2  0  0  0  2  2  0  2  2  0  2  0  0  2  0  0  2  0  2  0
 0  0  0  0  0  2  2  2  2  0  0  0  2  0  0  0  2  0  2  2  0  0  2  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+206x^20+328x^21+960x^22+1336x^23+1888x^24+2080x^25+2506x^26+2440x^27+2088x^28+1144x^29+846x^30+312x^31+191x^32+32x^33+6x^34+8x^35+10x^36+2x^38

The gray image is a code over GF(2) with n=104, k=14 and d=40.
This code was found by Heurico 1.16 in 3.39 seconds.