The generator matrix

 1  0  1  1 X^2  1 X^2+X  1  1  1  1  X  1  1 X^2+2  1 X^2+2 X^2 X+2  1  1 X^2  X  1  0  1  1
 0  1  1 X^2+X  1 X^2+X+1  1 X^2 X+3 X^2+3 X+2  1 X^2 X+3  1 X^2+X+2  1  1  1  3 X^2+X  1 X^2+2 X+3  1  0 X+1
 0  0  X  0 X+2  X  2 X+2 X^2+2 X^2 X^2+X  X X^2+X X^2+X+2 X^2+X+2 X+2  2 X^2 X^2+X X^2+X+2  0 X^2+X+2 X+2 X^2+2  0  X X+2
 0  0  0  2  0  2  2  2  2  0  0  2  2  2  2  2  2  2  0  2  0  0  0  0  2  2  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+351x^24+464x^25+928x^26+752x^27+824x^28+432x^29+256x^30+16x^31+51x^32+16x^34+4x^36+1x^40

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 0.203 seconds.