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

generates a code of length 27 over Z4[X]/(X^2+2) 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 0.016 seconds.