The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  X X^2 X^2  1
 0 X^2+2  0 X^2  0  2 X^2+2 X^2+2  0  2 X^2 X^2+2  0  0 X^2+2 X^2+2  2 X^2 X^2  2 X^2  0  2 X^2 X^2+2  0 X^2
 0  0 X^2+2 X^2  0 X^2 X^2  2  0 X^2 X^2  0  0 X^2+2 X^2  2  2 X^2+2  2  0  2  2 X^2+2 X^2  0 X^2+2  0
 0  0  0  2  0  0  2  0  2  2  0  2  2  2  0  2  2  2  0  2  0  2  2  0  0  0  2
 0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  0  2  2  0  0  2  0  0  0  0  2  0

generates a code of length 27 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+114x^24+80x^25+128x^26+352x^27+223x^28+80x^29+37x^32+8x^36+1x^44

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 6.64 seconds.