The generator matrix
1 1 1 1 1 1 1 1 1 1 1 X X X X 1 X 1 X X X X X X X X X
0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 2X 0 0 2X 2X 0 2X 2X 0 0
0 0 2X 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 2X 0 0 0 0 0 0 0 2X
0 0 0 2X 0 2X 2X 2X 0 0 0 0 0 2X 2X 0 2X 2X 2X 2X 2X 0 2X 2X 0 0 0
0 0 0 0 2X 2X 0 2X 2X 0 2X 0 2X 2X 0 2X 0 2X 2X 2X 0 0 0 2X 2X 2X 2X
generates a code of length 27 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 25.
Homogenous weight enumerator: w(x)=1x^0+14x^25+12x^26+208x^27+12x^28+4x^30+3x^32+2x^41
The gray image is a code over GF(2) with n=216, k=8 and d=100.
This code was found by Heurico 1.16 in 0.093 seconds.