The generator matrix

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

generates a code of length 27 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+330x^21+1699x^22+5634x^23+14086x^24+30516x^25+49271x^26+58230x^27+49984x^28+31458x^29+13905x^30+4952x^31+1487x^32+448x^33+117x^34+14x^35+8x^36+2x^39+2x^40

The gray image is a code over GF(2) with n=216, k=18 and d=84.
This code was found by Heurico 1.16 in 312 seconds.