The generator matrix
1 1 1 1 1 1 1 1 1 1 X X X X X X 1 1 X^2 1 1 X^2 X^2 X^2 X^2 X^2 X^2
0 2 0 0 0 2 2 2 0 0 0 2 2 0 2 2 0 0 0 0 2 2 2 2 0 2 0
0 0 2 0 2 2 2 0 0 0 2 2 0 2 2 0 0 0 2 2 2 0 0 2 2 2 0
0 0 0 2 2 0 2 2 0 2 2 0 0 0 2 2 0 2 2 2 0 0 2 2 0 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+40x^26+64x^27+14x^28+2x^30+1x^32+6x^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 0.031 seconds.