The generator matrix

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

generates a code of length 27 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+16x^27+8x^28+4x^29+2x^30+1x^32

The gray image is a code over GF(2) with n=216, k=5 and d=108.
This code was found by Heurico 1.16 in 1.05e-007 seconds.