The generator matrix

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

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+377x^24+408x^25+1024x^26+600x^27+930x^28+392x^29+288x^30+8x^31+49x^32+16x^34+2x^36+1x^40

The gray image is a code over GF(2) with n=216, k=12 and d=96.
This code was found by Heurico 1.16 in 0.203 seconds.