The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  X  X  2  2  2  X  1  X  X  1  2  1
 0 2X  0 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X  0 2X  0  0  0 2X
 0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0 2X  0 2X  0 2X 2X  0  0  0 2X  0 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+3x^26+50x^27+3x^28+1x^30+6x^31

The gray image is a code over GF(2) with n=216, k=6 and d=104.
This code was found by Heurico 1.16 in 0.015 seconds.