The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1  1
 0  2  0  0  0  0  0  2  0  2  0  2  0  2  0  2  0  2  2  0  2  0  0  2  2  0
 0  0  2  0  0  0  2  2  0  2  0  0  2  0  0  2  2  0  2  0  2  2  2  2  2  2
 0  0  0  2  0  0  2  0  0  2  2  2  2  2  2  2  2  2  2  2  0  2  0  2  0  2
 0  0  0  0  2  0  2  0  2  2  0  2  0  0  2  2  0  0  2  2  0  2  2  0  2  0
 0  0  0  0  0  2  2  0  2  0  2  2  0  2  0  2  2  0  0  2  2  0  0  0  2  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+11x^22+32x^24+173x^26+28x^28+5x^30+2x^32+3x^34+1x^48

The gray image is a code over GF(2) with n=104, k=8 and d=44.
This code was found by Heurico 1.16 in 0.0063 seconds.