The generator matrix

 1  0  0  0  0  1  1  1  1  2  1  1  1  0 X+2 X+2  1  1  X X+2  1  0  X  1  2  1  1
 0  1  0  0  0  2  1  3 X+1  1  X  X  X  1  1  1 X+2  2 X+2 X+2  X  X  1 X+3  0 X+3  2
 0  0  1  0  0 X+3 X+1 X+2 X+2 X+3  2  X  3  3  2 X+2 X+1 X+1  1  0  1  0 X+1  1  1  3  0
 0  0  0  1  0  1  X  3  0  3  2 X+3  1 X+2  1  X  2 X+2  3  1  2  1  2 X+1 X+2  0  2
 0  0  0  0  1  1  2 X+2  3 X+3  1 X+2  2  1  0  1  0 X+3 X+3  3 X+3  X  X X+1  1  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+52x^20+418x^21+960x^22+1770x^23+2354x^24+3614x^25+4561x^26+5104x^27+4535x^28+4030x^29+2562x^30+1554x^31+687x^32+362x^33+141x^34+36x^35+19x^36+8x^37

The gray image is a code over GF(2) with n=108, k=15 and d=40.
This code was found by Heurico 1.13 in 4.8 seconds.