The generator matrix

 1  0  0  0  1  1  1 X^2  1  1 X+2 X^2+X+2  1 X+2  1 X^2  2  0  1  1  1  1  1  X X^2+X+2  1  1
 0  1  0  0 X^2  3  1  1 X^2+1  3 X^2+2  1 X+2  1  2 X+2  0  1 X^2+X+1 X^2+X+2 X^2+2 X+1 X+3  1 X+2 X^2+X  0
 0  0  1  0 X^2+1  1 X^2 X^2+1 X+1 X^2+X  1 X+2 X^2+3 X+3 X^2+X+2  1  1  X  X  3 X^2+X X+1  1  0 X^2+X X+1  0
 0  0  0  1  1 X^2 X^2+1  3 X+1 X^2+X  3  3  X X+2 X^2+1 X+3 X+2 X^2+3  0 X^2+X+1  2  1  0 X^2+X+1  1 X+3 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+286x^22+1500x^23+3927x^24+7800x^25+11832x^26+14660x^27+12173x^28+7936x^29+3670x^30+1300x^31+344x^32+72x^33+20x^34+12x^35+3x^36

The gray image is a code over GF(2) with n=216, k=16 and d=88.
This code was found by Heurico 1.16 in 12.3 seconds.