The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+340x^23+1140x^24+1908x^25+3043x^26+3492x^27+3254x^28+1854x^29+924x^30+304x^31+75x^32+28x^33+7x^34+8x^35+2x^36+2x^37+2x^38

The gray image is a code over GF(2) with n=216, k=14 and d=92.
This code was found by Heurico 1.16 in 104 seconds.