The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+310x^21+1740x^22+5510x^23+14907x^24+28750x^25+50882x^26+56814x^27+51977x^28+29910x^29+14408x^30+4754x^31+1620x^32+386x^33+138x^34+26x^35+7x^36+4x^37

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 233 seconds.