The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+128x^22+64x^23+81x^24+192x^25+144x^26+192x^27+24x^28+64x^29+96x^30+21x^32+16x^34+1x^40

The gray image is a code over GF(2) with n=104, k=10 and d=44.
This code was found by Heurico 1.16 in 3.82 seconds.