The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+100x^19+513x^20+934x^21+1646x^22+2458x^23+3795x^24+4046x^25+5378x^26+4488x^27+4031x^28+2368x^29+1572x^30+810x^31+428x^32+134x^33+42x^34+16x^35+6x^37+2x^38

The gray image is a code over GF(2) with n=104, k=15 and d=38.
This code was found by Heurico 1.13 in 4.51 seconds.