The generator matrix

 1  0  1  1  1 2X 3X+2  1  1  1 X+2  1  1  1  1  X  1  1 2X+2  1  X  1  1  1  1  1  1
 0  1 X+1 X+2 2X+3  1  1 2X  3 3X+2  1 2X+1 3X+3 X+1 X+3 3X  3 2X+2  1  X  1 2X+1 3X+1 2X+1 3X+1 3X+1  0
 0  0 2X+2  2 2X 2X+2  0 2X+2  2  0  2 2X  2  0 2X  2 2X+2  2  2 2X+2 2X+2  2  2 2X+2 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+24x^24+164x^25+277x^26+162x^27+241x^28+80x^29+24x^30+42x^31+5x^32+2x^34+1x^38+1x^40

The gray image is a code over GF(2) with n=216, k=10 and d=96.
This code was found by Heurico 1.16 in 0.015 seconds.