The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  X  1 2X+2  1  X  X  1  1  2  X
 0  X  0 X+2  2 3X+2 2X+2  X  0 X+2 2X+2 3X 2X  X  X 2X+2 3X+2 3X+2 3X+2  X 2X X+2 3X  2 3X 2X+2  X
 0  0 2X+2  0  2  2 2X  2  0 2X  0  0  2  2 2X  2  2 2X+2  0 2X  2  0  0  2 2X 2X 2X+2
 0  0  0 2X  0  0 2X  0  0 2X 2X  0  0  0  0  0 2X 2X  0 2X 2X 2X 2X 2X 2X  0  0
 0  0  0  0 2X  0  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0  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+355x^24+640x^26+780x^28+224x^30+41x^32+4x^36+3x^40

The gray image is a code over GF(2) with n=216, k=11 and d=96.
This code was found by Heurico 1.16 in 12.7 seconds.