The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  2  1  X  X  1  X  X  1  1  1
 0  X  0  0  0  0  0  2  2  X X+2 X+2 X+2 X+2  0  X  X  2  0 X+2 X+2  2  2  X  X  0
 0  0  X  0  0  2 X+2  X  X  X  X X+2  0  X X+2 X+2  2  2  X X+2  X X+2 X+2  0 X+2  0
 0  0  0  X  0 X+2 X+2  X  2 X+2 X+2 X+2  X  0  2  X X+2 X+2  0  0 X+2  X  X X+2 X+2  2
 0  0  0  0  X  X  2 X+2  X X+2  2  0  X X+2  2 X+2  2 X+2  X X+2 X+2  2  0  X  X  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+35x^20+80x^21+102x^22+158x^23+236x^24+280x^25+286x^26+292x^27+235x^28+136x^29+79x^30+46x^31+37x^32+32x^33+12x^34+1x^38

The gray image is a code over GF(2) with n=104, k=11 and d=40.
This code was found by Heurico 1.16 in 0.0924 seconds.