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 2 0 2
0 2X+2 0 2X+2 2X 2 2X 2 0 2X+2 2X+2 2X+2 0 2X 2 2 2 0 2X 2X+2 2X 2 0 2X 2X+2 2 0
0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 2X 0 2X 2X 0 0 2X 0 0 0 2X 0
generates a code of length 27 over Z4[X]/(X^2+2) 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 0.016 seconds.