The generator matrix

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

generates a code of length 27 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+138x^22+802x^23+2036x^24+3758x^25+6320x^26+6778x^27+6242x^28+3780x^29+1964x^30+686x^31+183x^32+62x^33+8x^34+6x^35+2x^36+2x^38

The gray image is a code over GF(2) with n=216, k=15 and d=88.
This code was found by Heurico 1.16 in 3.22 seconds.