The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+248x^22+1686x^23+3867x^24+7472x^25+12241x^26+14076x^27+12822x^28+7804x^29+3482x^30+1398x^31+350x^32+64x^33+13x^34+8x^35+4x^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 12.1 seconds.