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.