The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X 2X+2  X  X  X 2X+2  X  0 2X
 0  X 2X+2 X+2  0 X+2 2X+2 3X 2X 3X+2  2 3X 2X 3X+2  2  X X+2  X 3X  X  0 2X+2 X+2  X 3X+2  2  X
 0  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X 2X 2X 2X 2X

generates a code of length 27 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+142x^26+92x^28+16x^30+3x^32+2x^34

The gray image is a code over GF(2) with n=216, k=8 and d=104.
This code was found by Heurico 1.16 in 6.87e-008 seconds.