The generator matrix

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

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+176x^23+229x^24+524x^25+824x^26+698x^27+766x^28+472x^29+197x^30+132x^31+24x^32+44x^33+2x^34+2x^35+4x^36+1x^38

The gray image is a code over GF(2) with n=216, k=12 and d=92.
This code was found by Heurico 1.16 in 0.125 seconds.