The generator matrix

 1  0  0  0  1  1  1  2  1  1  1  1  0  2  X X+2  1  1 3X 2X  1  1  1  0  1 3X+2  1
 0  1  0  0  0  1  1  1  2  X X+1 2X+3  1  1 3X 2X+2 3X+1 3X  1  1 2X 2X+1 X+1  1 X+1  X  0
 0  0  1  0  1  3  2  3  0 X+3  3 X+2 2X+2 3X+3  1  1 3X 3X 2X X+3 3X 2X+2 X+3  0 3X+3 3X+2  0
 0  0  0  1  1  2  3  1 X+3  0 3X+1 3X 3X+3  2 3X+1 3X X+3 2X+3 2X+1 X+3  2 3X 3X+1 3X+2  1  1 2X
 0  0  0  0 2X  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0  0  0  0 2X  0  0 2X 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+112x^21+821x^22+3068x^23+7006x^24+15048x^25+23964x^26+30400x^27+24657x^28+15666x^29+6701x^30+2500x^31+807x^32+260x^33+34x^34+16x^35+9x^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 45.5 seconds.