The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+12x^26+32x^27+12x^28+4x^30+3x^32

The gray image is a code over GF(2) with n=108, k=6 and d=52.
This code was found by Heurico 1.16 in 0.00584 seconds.