The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X  1  1  1  1  1  1 2X+2  1
 0  X  0  X 2X  0 3X  X 2X+2 3X+2 2X+2 3X+2  2 2X+2 X+2 3X+2  0 2X  X  2 3X+2  0 2X+2 X+2 2X  X  0
 0  0  X  X 2X+2 3X+2 3X+2 2X+2 2X+2 X+2  X 2X  0 3X+2 3X  2 2X X+2 2X+2 2X+2 3X+2  2  0 X+2 3X+2 2X+2  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+45x^24+166x^25+151x^26+320x^27+142x^28+148x^29+38x^30+4x^32+6x^33+2x^34+1x^50

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 0.016 seconds.