The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X X^2+2  X  X  X X^2+2  X  0  2
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2 X+2  2 X^2+X+2 X^2  X X^2+X  X X+2  X  0 X^2+2 X^2+X  X X^2+X+2 X^2  X
 0  0  2  2  2  0  0  2  2  2  0  0  0  0  2  2  0  2  2  0  2  2  2  2  2  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+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 -6.48e-008 seconds.