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  1  1  1  1  X
 0 2X  0  0  0  0  0 2X  0  0 2X 2X  0  0 2X 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X
 0  0 2X  0  0  0  0 2X  0 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0
 0  0  0 2X  0  0  0 2X 2X  0 2X  0 2X 2X  0 2X 2X  0 2X  0 2X  0 2X 2X 2X  0 2X
 0  0  0  0 2X  0 2X  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0
 0  0  0  0  0 2X 2X  0  0 2X 2X  0 2X  0 2X  0 2X  0 2X  0  0 2X 2X 2X  0  0 2X

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

Homogenous weight enumerator: w(x)=1x^0+21x^24+32x^26+384x^27+67x^28+6x^32+1x^52

The gray image is a code over GF(2) with n=216, k=9 and d=96.
This code was found by Heurico 1.16 in 0 seconds.