The generator matrix

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

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+116x^21+744x^22+3084x^23+7259x^24+14392x^25+25322x^26+29084x^27+25293x^28+15008x^29+7116x^30+2604x^31+788x^32+208x^33+34x^34+12x^35+3x^36+4x^37

The gray image is a code over GF(2) with n=216, k=17 and d=84.
This code was found by Heurico 1.16 in 45.8 seconds.