The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+302x^21+1679x^22+5618x^23+14497x^24+29542x^25+50944x^26+56250x^27+51652x^28+30284x^29+14225x^30+5102x^31+1552x^32+366x^33+94x^34+22x^35+10x^36+2x^37+2x^38

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 178 seconds.