The generator matrix

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

generates a code of length 27 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+18x^26+88x^27+10x^28+8x^29+1x^32+2x^34

The gray image is a code over GF(2) with n=216, k=7 and d=104.
This code was found by Heurico 1.16 in 0.015 seconds.