The generator matrix
1 1 1 1 1 1 1 1 1 1 X X X 1 1 X X X^2 X^2 X^2 X 1 X X 1 X^2 1
0 2 0 2 0 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 2 0 2 0 0 0 2
0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 2 0 2 0 2 2 0 0 0 2 0 2
generates a code of length 27 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 26.
Homogenous weight enumerator: w(x)=1x^0+3x^26+50x^27+3x^28+1x^30+6x^31
The gray image is a code over GF(2) with n=216, k=6 and d=104.
This code was found by Heurico 1.16 in 3.81e-009 seconds.