The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  X  1  X
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X  0 X^2+X  2 X^2+X X^2+2 X+2 X^2+2  X  0 X^2 X^2+X X^2+2 X+2  2 X^2+X  2 X^2+X X+2 X^2+X
 0  0 X^2+2  0 X^2 X^2  2 X^2  2  2 X^2 X^2+2 X^2+2 X^2+2  0  2  0 X^2+2 X^2+2  2 X^2+2  2 X^2 X^2  2  2  0
 0  0  0  2  2  0  2  2  0  2  0  0  2  2  2  0  2  0  2  0  0  2  2  2  2  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+79x^24+64x^25+141x^26+512x^27+82x^28+64x^29+50x^30+29x^32+1x^34+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 0.031 seconds.