The generator matrix

 1  0  0  0  0  1  1  1  1  2  0  1  1  0  1  2  1  1  X  1  1  1  1 X+2  2  1  X
 0  1  0  0  0  0  2  0  0  2  1  3 X+3  1 X+3 X+2 X+1 X+2  1 X+2  1  1  X  1  1 X+3  1
 0  0  1  0  0  0  1  2 X+1  1 X+2  1  X X+3  0  1  2  X  3 X+3 X+3 X+2  3 X+1  1  X X+3
 0  0  0  1  0  1  1  X  0  3  2 X+3 X+3 X+2 X+2  0  X  1  1 X+1  2  1 X+2 X+1  X  X  2
 0  0  0  0  1  1  X X+1 X+1 X+3  1  1  2  2  1  3  X  X X+1 X+1  1 X+3  X  X  2 X+2 X+3
 0  0  0  0  0  2  0  0  2  2  2  2  0  0  0  0  2  2  0  2  0  0  2  0  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+239x^20+814x^21+1849x^22+3286x^23+4576x^24+7822x^25+8659x^26+10826x^27+8601x^28+8142x^29+4961x^30+3194x^31+1530x^32+626x^33+273x^34+102x^35+28x^36+4x^37+2x^38+1x^40

The gray image is a code over GF(2) with n=108, k=16 and d=40.
This code was found by Heurico 1.13 in 18 seconds.