The generator matrix

 1  0  0  0  1  1  1 2X+2  1  1  1  1 3X 3X+2  0 3X  1  1 X+2 2X 2X+2 3X+2  1  2  1 2X  1
 0  1  0  0  0  1  1  1 2X+2  X X+1 2X+1  1 2X  1 3X+2 X+2 2X+2  1  1  1 2X 3X+3  1 3X  1  0
 0  0  1  0  1 2X+3 2X+2 2X+3  0 3X+3 2X+3 3X+2 3X  1 3X+3  1  0  X 2X+2  1 2X  1 3X+3 3X+2 3X+1 3X+2  0
 0  0  0  1  1 2X+2 2X+3  1 3X+3  0 3X+1 3X+2 2X+1  3 2X+2 2X+2  X  3 3X+2 3X+3 X+3 3X+3 3X+2 X+1  X 2X+1  0
 0  0  0  0 2X  0 2X 2X 2X  0 2X  0  0  0 2X 2X 2X  0 2X  0 2X 2X 2X  0  0  0 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+112x^21+872x^22+2876x^23+7142x^24+15286x^25+23662x^26+30380x^27+24712x^28+15734x^29+6708x^30+2436x^31+845x^32+226x^33+54x^34+20x^35+4x^36+2x^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 46.3 seconds.