The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+57x^18+90x^19+204x^20+274x^21+728x^22+1236x^23+1844x^24+2448x^25+2522x^26+2576x^27+1848x^28+1196x^29+741x^30+316x^31+187x^32+48x^33+45x^34+6x^35+12x^36+2x^37+2x^38+1x^46

The gray image is a code over GF(2) with n=104, k=14 and d=36.
This code was found by Heurico 1.16 in 6.42 seconds.