The generator matrix

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

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+6x^26+48x^27+6x^28+1x^32+2x^38

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 0.0029 seconds.