The generator matrix

 1  0  0  1  1  1  X  2  1  1  1  2  X  1  1  X  1 X+2  1 X+2  X  1  1  1  1  0  1
 0  1  0  1  0 X+3  1  X X+2  1 X+2  1  1  3  3  1  0  1 X+1  X  1 X+2  0 X+2 X+1  X  2
 0  0  1  1  1  0  1  1  X  1 X+1  0 X+3  0  1  2  X  1 X+2  1  0  2 X+3 X+1  2  X  X
 0  0  0  X  0 X+2  2  X  2 X+2  0  2 X+2  0  0  X X+2 X+2  0  X X+2  X X+2  X X+2 X+2  X
 0  0  0  0  X  0  2 X+2 X+2  X  2  X X+2  0 X+2  2  0  0 X+2  2 X+2  X  2 X+2  X  0  X
 0  0  0  0  0  2  2  2  2  2  2  2  0  2  2  0  0  2  0  0  2  2  0  0  0  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+44x^20+244x^21+401x^22+942x^23+1174x^24+2010x^25+1969x^26+2772x^27+1956x^28+2104x^29+1215x^30+934x^31+333x^32+186x^33+62x^34+24x^35+12x^36+1x^50

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 3.64 seconds.