The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+6x^26+24x^28+192x^29+24x^30+7x^32+2x^42

The gray image is a code over GF(2) with n=232, k=8 and d=104.
This code was found by Heurico 1.16 in -3.24e-008 seconds.