The generator matrix

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

generates a code of length 27 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+144x^24+400x^26+340x^28+96x^30+42x^32+1x^48

The gray image is a code over GF(2) with n=216, k=10 and d=96.
This code was found by Heurico 1.16 in 0.015 seconds.