The generator matrix

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

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+153x^24+236x^25+560x^26+196x^27+541x^28+184x^29+138x^30+20x^31+8x^32+4x^33+6x^34+1x^36

The gray image is a code over GF(2) with n=216, k=11 and d=96.
This code was found by Heurico 1.16 in 0.015 seconds.