The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+176x^20+492x^22+638x^24+384x^25+1736x^26+1280x^27+1804x^28+384x^29+688x^30+424x^32+152x^34+28x^36+4x^38+1x^48

The gray image is a code over GF(2) with n=108, k=13 and d=40.
This code was found by Heurico 1.16 in 1.58 seconds.