The generator matrix

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

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+94x^22+826x^23+1878x^24+4038x^25+5640x^26+7694x^27+5918x^28+4086x^29+1662x^30+694x^31+153x^32+66x^33+12x^34+2x^35+2x^36+2x^37

The gray image is a code over GF(2) with n=216, k=15 and d=88.
This code was found by Heurico 1.16 in 3.56 seconds.