The generator matrix

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

generates a code of length 26 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+56x^26+5x^28+1x^32+1x^36

The gray image is a code over GF(2) with n=208, k=6 and d=104.
This code was found by Heurico 1.16 in -6.48e-008 seconds.