The generator matrix

 1  0  0  1  1  1 2X+2  1  1  X  1 3X+2 3X  1  1  1  1  1  1  1  1  0  X  1 3X+2 3X  1
 0  1  0 2X  3 2X+3  1  2  X  1 3X+1  1 2X+2 2X+1 X+3 X+2  X 2X X+1 3X+2  1  1  1 3X+3  1  1 2X
 0  0  1 3X+1 X+1 2X X+1  X X+3 2X+2 3X+3  1  1 X+2 2X+2  X 2X+3  1 3X+2  0  3 3X+2 3X+2  3 X+1  3 2X

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

Homogenous weight enumerator: w(x)=1x^0+206x^24+780x^25+654x^26+1096x^27+392x^28+600x^29+264x^30+72x^31+9x^32+12x^33+10x^34

The gray image is a code over GF(2) with n=216, k=12 and d=96.
This code was found by Heurico 1.16 in 0.062 seconds.