The generator matrix

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

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+86x^20+96x^21+239x^22+442x^23+615x^24+896x^25+1109x^26+1194x^27+1115x^28+976x^29+609x^30+398x^31+228x^32+80x^33+86x^34+14x^35+3x^36+4x^38+1x^50

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 1.19 seconds.