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

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+9x^24+24x^25+22x^26+400x^27+22x^28+24x^29+9x^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 0.016 seconds.