The generator matrix

 1  0  1  1  1 X+2  1  1 X+2  1  1  0  1  1  1  1  1  1  1  1  2  X  2  X  1  1  X
 0  1 X+1 X+2  3  1  0 X+1  1 X+2  3  1  2  X X+3  1  2  X X+3  1  1  1  1  1  0 X+2 X+2
 0  0  2  2  0  2  2  0  0  0  2  2  2  0  2  0  0  2  0  2  2  0  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+46x^26+32x^27+44x^28+2x^30+1x^32+2x^36

The gray image is a code over GF(2) with n=108, k=7 and d=52.
This code was found by Heurico 1.16 in 0.00475 seconds.