The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+240x^22+1710x^23+3853x^24+7496x^25+12053x^26+14438x^27+12524x^28+7946x^29+3458x^30+1338x^31+372x^32+92x^33+9x^34+2x^35+2x^36+2x^37

The gray image is a code over GF(2) with n=216, k=16 and d=88.
This code was found by Heurico 1.16 in 12.3 seconds.