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

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+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 6.66 seconds.