The generator matrix

 1  0  0  1  1  1  2  1  1  X  1 X^2+2  1 X^2+X+2  1  X X^2+X  1  1  0 X^2+X X^2  1 X^2 X^2+X+2 X^2  1
 0  1  0  2 X^2+1 X^2+3  1 X^2  X  1 X+3  1  3 X+2 X^2+X+2 X^2+2  1 X+2 X^2+X+1 X^2+X+2  1 X^2 X^2+2  1  1  1  2
 0  0  1 X+3 X+1  2 X+3  X X^2+X+1 X^2+2 X^2+X+3  1 X^2+X+2  1 X^2+2  1  3 X^2+1  3  1 X+2  1  1  X X+1 X^2+X X^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+176x^24+752x^25+829x^26+958x^27+477x^28+508x^29+241x^30+110x^31+34x^32+8x^33+2x^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.