The generator matrix

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

generates a code of length 27 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+390x^23+1046x^24+1870x^25+3121x^26+3616x^27+3184x^28+1776x^29+882x^30+362x^31+77x^32+50x^33+5x^34+4x^36

The gray image is a code over GF(2) with n=216, k=14 and d=92.
This code was found by Heurico 1.16 in 29.3 seconds.