The generator matrix

 1  0  0  1  1  1  0 X^2  1  1 X^2+X+2  1  X  1  1 X+2  1  2  1  1 X^2  0  1 X^2+X  1 X+2  1
 0  1  0 X^2 X^2+1  1  1  X  0 X^2+2  1 X^2+X+3  1 X+3  X  2 X^2+1  1 X^2+3  X  1  1 X^2+X+2  1  2  1  0
 0  0  1 X^2+X+1 X+1 X^2 X+1  1 X^2+X  3  X X+3 X^2+X+1 X^2  1  1  X  1  1 X^2+X+3 X^2+X X^2+X+3 X^2+1 X^2 X+2 X^2+1  0
 0  0  0  2  2  0  2  2  2  0  2  0  0  2  0  2  0  2  2  2  2  0  2  2  0  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+104x^23+549x^24+1120x^25+1456x^26+1856x^27+1453x^28+988x^29+444x^30+132x^31+58x^32+20x^33+4x^34+4x^35+3x^36

The gray image is a code over GF(2) with n=216, k=13 and d=92.
This code was found by Heurico 1.16 in 0.219 seconds.