The generator matrix

 1  0  0  1  1  1 3X+2 X+2 3X  1  1  1  1  1  X 2X  1 X+2  1  1 3X X+2  1 2X+2  2 3X 3X+2
 0  1  0  0  3 X+1  1 2X  1 3X 3X 2X+1 3X+1  3  1  1 3X+1 X+2 3X+2 2X+2  1 2X 3X  1  1  1 3X
 0  0  1 X+1 X+1  0 3X+3  1  X  X 2X+3 2X+2 3X  1  1  1  1  1 X+3 3X+1  2  1 X+1 3X 3X+3 3X  1
 0  0  0 2X+2  2 2X 2X+2 2X+2 2X+2  2  0 2X+2 2X 2X  0 2X+2 2X+2  2 2X+2  0  0 2X  0 2X  0  2 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+358x^23+1041x^24+2016x^25+3005x^26+3668x^27+3035x^28+1872x^29+904x^30+366x^31+74x^32+32x^33+1x^34+8x^35+1x^36+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 16.4 seconds.