The generator matrix

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

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+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.