The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+7x^24+110x^26+7x^28+2x^34+1x^36

The gray image is a code over GF(2) with n=208, k=7 and d=96.
This code was found by Heurico 1.16 in -3.24e-008 seconds.