The generator matrix
1 1 1 1 1 1 1 1 1 X 1 X 1 X 1 X X X 1 1 1 1 X X X^2 0 X^2
0 X^2+2 0 X^2+2 2 X^2 2 X^2 0 X^2+2 X^2+2 X^2+2 0 2 X^2 X^2 X^2 0 2 X^2+2 2 X^2 0 2 X^2+2 X^2 0
0 0 2 2 2 2 0 0 0 0 2 2 2 2 0 2 0 2 2 0 0 2 0 0 0 2 0
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+60x^26+60x^28+4x^30+3x^32
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.