The generator matrix

 1  0  0  1  1  1  2  1  1  X  1  1 X+2  X  1  1  2  1 2X+2 3X+2  X  1  1  1 2X+2  1  1
 0  1  0 2X 2X+3  3  1 2X+2  X  1 3X+1 2X+1  1 3X X+1 2X  X X+2  1  1  1 3X+3 3X 3X+1  1 X+2  2
 0  0  1 3X+1 X+1 2X X+1  X 3X+3  2 X+3 3X+2 2X+1  1 2X 2X+1  1  3 3X 3X+3 3X 2X+1  2  X  3 X+2  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+120x^24+958x^25+600x^26+1016x^27+421x^28+678x^29+147x^30+116x^31+18x^32+16x^33+5x^34

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 0.063 seconds.