The generator matrix
1 1 1 1 1 1 1 1 X 0 1 X X^2+2 1 1 1 X 2 X X^2 1 1 1 1 X X 1
0 X X^2+2 X^2+X 2 X^2+X+2 X^2 X+2 X^2+X X 0 X+2 X X^2+2 X^2+X X+2 X^2+X+2 X X X 2 X^2 X^2+X+2 X 0 X^2+2 X^2+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+18x^26+88x^27+10x^28+8x^29+1x^32+2x^34
The gray image is a code over GF(2) with n=216, k=7 and d=104.
This code was found by Heurico 1.16 in 0.015 seconds.