The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  1  0  1  1  1  1  1  X  X  1  X X+2  1  X
 0  1  1  0  1  1  X X+3  1 X+2  1 X+3  0  1 X+1  3  X X+3  X  1  1 X+2  1  1  X  2
 0  0  X  0  0  0  0  0  0  2  2  X  X  X  0 X+2  2 X+2  X X+2 X+2  2  0  2  X  0
 0  0  0  X  0  0  X  2  X  2 X+2  0  0  0 X+2 X+2  2 X+2 X+2  2  0  X  2  2  2  X
 0  0  0  0  X  0  0  X  2  2  0  2 X+2  X X+2  2 X+2  X  0  2  2 X+2 X+2 X+2  2  2
 0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  2  0  2  2  0  0  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+189x^20+72x^21+506x^22+512x^23+1132x^24+880x^25+1502x^26+1120x^27+1102x^28+392x^29+502x^30+96x^31+131x^32+50x^34+5x^36

The gray image is a code over GF(2) with n=104, k=13 and d=40.
This code was found by Heurico 1.16 in 1.16 seconds.