The generator matrix

 1  1  1  1  1  1  1  1  X  0  1  X  2  1  1  1  X 2X  X 2X+2  1  1  1  1  X  X  1
 0  X  2 3X+2 2X X+2 2X+2 3X 3X+2  X  0 3X  X  2 3X+2 3X X+2  X  X  X 2X 2X+2 X+2  X  0  2  2

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