The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+166x^23+238x^24+448x^25+781x^26+854x^27+846x^28+416x^29+136x^30+130x^31+33x^32+32x^33+10x^34+2x^35+2x^36+1x^42

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 49.4 seconds.