The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+120x^19+619x^20+1594x^21+3245x^22+6230x^23+9612x^24+15394x^25+18151x^26+20814x^27+18304x^28+15526x^29+9935x^30+6370x^31+3031x^32+1318x^33+505x^34+194x^35+81x^36+24x^37+4x^38

The gray image is a code over GF(2) with n=108, k=17 and d=38.
This code was found by Heurico 1.13 in 68.5 seconds.