The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+106x^24+128x^26+248x^28+12x^32+16x^36+1x^48

The gray image is a code over GF(2) with n=108, k=9 and d=48.
This code was found by Heurico 1.16 in 17.8 seconds.