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

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+17x^24+8x^25+14x^26+432x^27+14x^28+8x^29+17x^30+1x^54

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 0.015 seconds.