The generator matrix

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

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+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.