The generator matrix

 1  0  0  1  1  1  0  1  1  X X+2  1  0  1 X+2  X  1  1  0  1  1  1  1  1  1 X+2  1
 0  1  0  1  X X+3  1  0 X+3  1  X  2  1 X+1  1  1 X+1  1  2 X+1 X+2 X+2  3  X X+2  2  1
 0  0  1  1  1  0 X+3  X  X  1  1  1  X X+1  X  X  X  X  1 X+3  X X+3 X+2  0  X  1  1
 0  0  0  X  0 X+2 X+2  X  2  2 X+2  0 X+2  0 X+2  2  X  0 X+2 X+2  X X+2 X+2 X+2  2  2  0
 0  0  0  0  2  0  0  2  2  2  2  2  2  2  0  2  2  0  2  2  0  0  2  0  0  0  2
 0  0  0  0  0  2  0  0  0  2  0  2  0  2  0  2  0  0  2  2  2  2  2  0  2  2  2
 0  0  0  0  0  0  2  2  0  2  2  2  2  0  0  0  0  2  0  0  2  2  2  0  2  0  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+56x^20+232x^21+374x^22+784x^23+1301x^24+1884x^25+2373x^26+2376x^27+2351x^28+1908x^29+1301x^30+800x^31+381x^32+196x^33+47x^34+8x^35+5x^36+4x^37+1x^38+1x^48

The gray image is a code over GF(2) with n=108, k=14 and d=40.
This code was found by Heurico 1.16 in 3.31 seconds.