The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+79x^24+404x^25+371x^26+384x^27+363x^28+344x^29+75x^30+4x^32+20x^33+1x^34+1x^36+1x^38

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 0.031 seconds.