The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+153x^24+236x^25+560x^26+196x^27+541x^28+184x^29+138x^30+20x^31+8x^32+4x^33+6x^34+1x^36

The gray image is a code over GF(2) with n=216, k=11 and d=96.
This code was found by Heurico 1.16 in 0.032 seconds.