The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+303x^26+156x^28+48x^30+3x^32+1x^42

The gray image is a code over GF(2) with n=216, k=9 and d=104.
This code was found by Heurico 1.16 in 118 seconds.